 Halliday/Resnick/Walker Fundamentals of Physics 8th edition

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Halliday/Resnick/Walker Fundamentals of Physics 8th edition
Classroom Response System Questions Chapter 4 Motion in Two and Three Dimensions Reading Quiz Questions

4.2.1. Which one of the following statements concerning the displacement of an object is false?
a) Displacement is a vector quantity that points from the initial position of an object to its final position. b) The magnitude of an object’s displacement is always equal to the distance it traveled from its initial position to its final position. c) The magnitude of an object’s displacement is the shortest distance from its initial position to its final position. d) The direction of an object’s displacement is indicated by an arrow that begins on the initial position of the object and ends on its final position. e) The length of the arrow representing an object’s displacement is proportional to its magnitude.

4.2.1. Which one of the following statements concerning the displacement of an object is false?
a) Displacement is a vector quantity that points from the initial position of an object to its final position. b) The magnitude of an object’s displacement is always equal to the distance it traveled from its initial position to its final position. c) The magnitude of an object’s displacement is the shortest distance from its initial position to its final position. d) The direction of an object’s displacement is indicated by an arrow that begins on the initial position of the object and ends on its final position. e) The length of the arrow representing an object’s displacement is proportional to its magnitude.

4. 2. 2. At time t1 = 0 s, the position vector of a sailboat is
At time t1 = 0 s, the position vector of a sailboat is Later, at time t2, the sailboat has a position vector Which of the following expressions correctly indicates the displacement of the sailboat during the time interval, t2  t1? a) b) c) d) e)

4. 2. 2. At time t1 = 0 s, the position vector of a sailboat is
At time t1 = 0 s, the position vector of a sailboat is Later, at time t2, the sailboat has a position vector Which of the following expressions correctly indicates the displacement of the sailboat during the time interval, t2  t1? a) b) c) d) e)

4. 2. 3. A delivery truck leaves a warehouse and travels 3. 20 km east
A delivery truck leaves a warehouse and travels 3.20 km east. The truck makes a right turn and travels 2.45 km south to arrive at its destination. What is the magnitude and direction of the truck’s displacement from the warehouse? a) km, 37.4 south of east b) km, 52.5 south of east c) km, 37.8 south of east d) km, 45.0 south of east e) km, 52.5 south of east

4. 2. 3. A delivery truck leaves a warehouse and travels 3. 20 km east
A delivery truck leaves a warehouse and travels 3.20 km east. The truck makes a right turn and travels 2.45 km south to arrive at its destination. What is the magnitude and direction of the truck’s displacement from the warehouse? a) km, 37.4 south of east b) km, 52.5 south of east c) km, 37.8 south of east d) km, 45.0 south of east e) km, 52.5 south of east

Which one of the following quantities is an object’s displacement divided by the elapsed time of the displacement? a) average velocity b) instantaneous velocity c) average displacement d) average acceleration e) instantaneous acceleration

Which one of the following quantities is an object’s displacement divided by the elapsed time of the displacement? a) average velocity b) instantaneous velocity c) average displacement d) average acceleration e) instantaneous acceleration

While on a one-hour trip, a small boat travels 32 km north and then travels 45 km east. What is the magnitude of the boat's average velocity for the one-hour trip? a) 39 km/h b) 55 km/h c) 77 km/h d) 89 km/h e) 96 km/h

While on a one-hour trip, a small boat travels 32 km north and then travels 45 km east. What is the magnitude of the boat's average velocity for the one-hour trip? a) 39 km/h b) 55 km/h c) 77 km/h d) 89 km/h e) 96 km/h

While on a one-hour trip, a small boat travels 32 km north and then travels 45 km east. What is the direction of the boat's average velocity for the one-hour trip? a) 45 north of east b) 54 north of east c) 35 north of east d) 27 north of east e) due east

While on a one-hour trip, a small boat travels 32 km north and then travels 45 km east. What is the direction of the boat's average velocity for the one-hour trip? a) 45 north of east b) 54 north of east c) 35 north of east d) 27 north of east e) due east

Complete the following statement: The direction of the instantaneous velocity of a particle is a) tangent to the path of the particle. b) the same as the direction of the average velocity vector. c) perpendicular to the path of the particle. d) the same as the direction of the acceleration of the particle. e) perpendicular to the direction of the acceleration of the particle.

Complete the following statement: The direction of the instantaneous velocity of a particle is a) tangent to the path of the particle. b) the same as the direction of the average velocity vector. c) perpendicular to the path of the particle. d) the same as the direction of the acceleration of the particle. e) perpendicular to the direction of the acceleration of the particle.

4. 3. 5. A truck drives due south for 1. 8 km in 2. 0 minutes
A truck drives due south for 1.8 km in 2.0 minutes. Then, the truck turns and drives due west for 1.8 km in 2.0 minutes. Which one of the following statements is correct? a) The average speed for the two segments is the same. The average velocity for the two segments is the same. b) The average speed for the two segments is not the same. The average velocity for the two segments is the same. c) The average speed for the two segments is the same. The average velocity for the two segments is not the same. d) The average speed for the two segments is not the same. The average velocity for the two segments is not the same.

4. 3. 5. A truck drives due south for 1. 8 km in 2. 0 minutes
A truck drives due south for 1.8 km in 2.0 minutes. Then, the truck turns and drives due west for 1.8 km in 2.0 minutes. Which one of the following statements is correct? a) The average speed for the two segments is the same. The average velocity for the two segments is the same. b) The average speed for the two segments is not the same. The average velocity for the two segments is the same. c) The average speed for the two segments is the same. The average velocity for the two segments is not the same. d) The average speed for the two segments is not the same. The average velocity for the two segments is not the same.

4.4.1. Which of the following is not a vector?
a) position b) displacement c) average velocity d) centripetal acceleration e) range

4.4.1. Which of the following is not a vector?
a) position b) displacement c) average velocity d) centripetal acceleration e) range

Which one of the following quantities is the change in object’s velocity divided by the elapsed time as the elapsed time becomes very small? a) average velocity b) instantaneous velocity c) average displacement d) average acceleration e) instantaneous acceleration

Which one of the following quantities is the change in object’s velocity divided by the elapsed time as the elapsed time becomes very small? a) average velocity b) instantaneous velocity c) average displacement d) average acceleration e) instantaneous acceleration

4.4.3. How is the direction of the average acceleration determined?
a) The direction of the average acceleration is the same as that of the displacement vector. b) The direction of the average acceleration is the same as that of the instantaneous velocity vector. c) The direction of the average acceleration is that of the vector subtraction of the initial velocity from the final velocity. d) The direction of the average acceleration is the same as that of the average velocity vector. e) The direction of the average acceleration is that of the vector addition of the initial velocity from the final velocity.

4.4.3. How is the direction of the average acceleration determined?
a) The direction of the average acceleration is the same as that of the displacement vector. b) The direction of the average acceleration is the same as that of the instantaneous velocity vector. c) The direction of the average acceleration is that of the vector subtraction of the initial velocity from the final velocity. d) The direction of the average acceleration is the same as that of the average velocity vector. e) The direction of the average acceleration is that of the vector addition of the initial velocity from the final velocity.

A football is kicked at an angle 25 with respect to the horizontal. Which one of the following statements best describes the acceleration of the football during this event if air resistance is neglected? a) The acceleration is zero m/s2 at all times. b) The acceleration is zero m/s2 when the football has reached the highest point in its trajectory. c) The acceleration is positive as the football rises, and it is negative as the football falls. d) The acceleration starts at 9.8 m/s2 and drops to some constant lower value as the ball approaches the ground. e) The acceleration is 9.8 m/s2 at all times.

A football is kicked at an angle 25 with respect to the horizontal. Which one of the following statements best describes the acceleration of the football during this event if air resistance is neglected? a) The acceleration is zero m/s2 at all times. b) The acceleration is zero m/s2 when the football has reached the highest point in its trajectory. c) The acceleration is positive as the football rises, and it is negative as the football falls. d) The acceleration starts at 9.8 m/s2 and drops to some constant lower value as the ball approaches the ground. e) The acceleration is 9.8 m/s2 at all times.

A baseball is hit upward and travels along a parabolic arc before it strikes the ground. Which one of the following statements is necessarily true? a) The velocity of the ball is a maximum when the ball is at the highest point in the arc. b) The x-component of the velocity of the ball is the same throughout the ball's flight. c) The acceleration of the ball decreases as the ball moves upward. d) The velocity of the ball is zero m/s when the ball is at the highest point in the arc. e) The acceleration of the ball is zero m/s2 when the ball is at the highest point in the arc.

A baseball is hit upward and travels along a parabolic arc before it strikes the ground. Which one of the following statements is necessarily true? a) The velocity of the ball is a maximum when the ball is at the highest point in the arc. b) The x-component of the velocity of the ball is the same throughout the ball's flight. c) The acceleration of the ball decreases as the ball moves upward. d) The velocity of the ball is zero m/s when the ball is at the highest point in the arc. e) The acceleration of the ball is zero m/s2 when the ball is at the highest point in the arc.

4. 5. 3. Two cannons are mounted on a high cliff
Two cannons are mounted on a high cliff. Cannon A fires balls with twice the initial velocity of cannon B. Both cannons are aimed horizontally and fired. How does the horizontal range of cannon A compare to that of cannon B? a) The range for both balls will be the same b) The range of the cannon ball B is about 0.7 that of cannon ball A. c) The range of the cannon ball B is about 1.4 times that of cannon ball A. d) The range of the cannon ball B is about 2 times that of cannon ball A. e) The range of the cannon ball B is about 0.5 that of cannon ball A.

4. 5. 3. Two cannons are mounted on a high cliff
Two cannons are mounted on a high cliff. Cannon A fires balls with twice the initial velocity of cannon B. Both cannons are aimed horizontally and fired. How does the horizontal range of cannon A compare to that of cannon B? a) The range for both balls will be the same b) The range of the cannon ball B is about 0.7 that of cannon ball A. c) The range of the cannon ball B is about 1.4 times that of cannon ball A. d) The range of the cannon ball B is about 2 times that of cannon ball A. e) The range of the cannon ball B is about 0.5 that of cannon ball A.

Which one of the following statements concerning the range of a football is true if the football is kicked at an angle  with an initial speed v0? a) The range is independent of initial speed v0. b) The range is only dependent on the initial speed v0. c) The range is independent of the angle. d) The range is only dependent on the angle. e) The range is dependent on both the initial speed v0 and the angle.

Which one of the following statements concerning the range of a football is true if the football is kicked at an angle  with an initial speed v0? a) The range is independent of initial speed v0. b) The range is only dependent on the initial speed v0. c) The range is independent of the angle. d) The range is only dependent on the angle. e) The range is dependent on both the initial speed v0 and the angle.

4.5.5. Complete the following statement: In projectile motion,
a) the horizontal motion depends on the vertical motion. b) the vertical motion depends on the horizontal motion. c) the horizontal acceleration depends on the vertical acceleration. d) the horizontal motion and the vertical motion are independent of each other. e) the vertical acceleration depends on the horizontal acceleration.

4.5.5. Complete the following statement: In projectile motion,
a) the horizontal motion depends on the vertical motion. b) the vertical motion depends on the horizontal motion. c) the horizontal acceleration depends on the vertical acceleration. d) the horizontal motion and the vertical motion are independent of each other. e) the vertical acceleration depends on the horizontal acceleration.

An airplane is flying horizontally at a constant velocity when a package is dropped from its cargo bay. Assuming no air resistance, which one of the following statements is correct? a) The package follows a curved path that lags behind the airplane. b) The package follows a straight line path that lags behind the airplane. c) The package follows a straight line path, but it is always vertically below the airplane. d) The package follows a curved path, but it is always vertically below the airplane. e) The package follows a curved path, but its horizontal position varies depending on the velocity of the airplane.

An airplane is flying horizontally at a constant velocity when a package is dropped from its cargo bay. Assuming no air resistance, which one of the following statements is correct? a) The package follows a curved path that lags behind the airplane. b) The package follows a straight line path that lags behind the airplane. c) The package follows a straight line path, but it is always vertically below the airplane. d) The package follows a curved path, but it is always vertically below the airplane. e) The package follows a curved path, but its horizontal position varies depending on the velocity of the airplane.

4. 6. 1. A ball is launched with an initial velocity as shown
A ball is launched with an initial velocity as shown. Which one of the following arrows best represents the direction of the acceleration at point A? a) b) c) d) e) The acceleration at point A is zero m/s2.

4. 6. 1. A ball is launched with an initial velocity as shown
A ball is launched with an initial velocity as shown. Which one of the following arrows best represents the direction of the acceleration at point A? a) b) c) d) e) The acceleration at point A is zero m/s2.

4. 6. 2. A ball is launched with an initial velocity as shown
A ball is launched with an initial velocity as shown. Which one of the following arrows best represents the direction of the acceleration at point B? a) b) c) d) e) The velocity at point B is zero m/s.

4. 6. 2. A ball is launched with an initial velocity as shown
A ball is launched with an initial velocity as shown. Which one of the following arrows best represents the direction of the acceleration at point B? a) b) c) d) e) The velocity at point B is zero m/s.

4. 6. 3. A ball is launched with an initial velocity as shown
A ball is launched with an initial velocity as shown. Which one of the following arrows best represents the direction of the velocity at point C? a) b) c) d) e) The velocity at point C is zero m/s.

4. 6. 3. A ball is launched with an initial velocity as shown
A ball is launched with an initial velocity as shown. Which one of the following arrows best represents the direction of the velocity at point C? a) b) c) d) e) The velocity at point C is zero m/s.

4. 6. 4. A ball is launched with an initial velocity as shown
A ball is launched with an initial velocity as shown. Which one of the following arrows best represents the direction of the acceleration at point B? a) b) c) d) e) The acceleration at point B is zero m/s2.

4. 6. 4. A ball is launched with an initial velocity as shown
A ball is launched with an initial velocity as shown. Which one of the following arrows best represents the direction of the acceleration at point B? a) b) c) d) e) The acceleration at point B is zero m/s2.

4. 6. 5. A ball is launched with an initial velocity as shown
A ball is launched with an initial velocity as shown. Which one of the following graphs best represents the horizontal position, x, of the ball versus elapsed time?

4. 6. 5. A ball is launched with an initial velocity as shown
A ball is launched with an initial velocity as shown. Which one of the following graphs best represents the horizontal position, x, of the ball versus elapsed time?

4. 6. 6. A ball is launched with an initial velocity as shown
A ball is launched with an initial velocity as shown. Which one of the following graphs best represents the vertical position, y, of the ball versus elapsed time?

4. 6. 6. A ball is launched with an initial velocity as shown
A ball is launched with an initial velocity as shown. Which one of the following graphs best represents the vertical position, y, of the ball versus elapsed time?

4. 6. 7. A ball is launched with an initial velocity as shown
A ball is launched with an initial velocity as shown. Which one of the following graphs best represents the y component of the velocity of the ball versus elapsed time?

4. 6. 7. A ball is launched with an initial velocity as shown
A ball is launched with an initial velocity as shown. Which one of the following graphs best represents the y component of the velocity of the ball versus elapsed time?

A professional golfer’s club strikes a ball on a tee and launches the ball at an angle of 40. Which one of the following statements concerning the acceleration of the ball is true, if the effects of air resistance are ignored? a) While the ball is in the air, its acceleration is zero m/s2. b) At the highest point of the ball’s flight, its acceleration is instantaneously equal to zero m/s2. c) As it is rising, its acceleration decreases from 9.8 m/s2 to zero m/s2 at its highest point. d) The acceleration is equal to (9.8 m/s2)(sin 40) = 6.3 m/s2. e) While the ball is in the air, its acceleration is 9.8 m/s2.

A professional golfer’s club strikes a ball on a tee and launches the ball at an angle of 40. Which one of the following statements concerning the acceleration of the ball is true, if the effects of air resistance are ignored? a) While the ball is in the air, its acceleration is zero m/s2. b) At the highest point of the ball’s flight, its acceleration is instantaneously equal to zero m/s2. c) As it is rising, its acceleration decreases from 9.8 m/s2 to zero m/s2 at its highest point. d) The acceleration is equal to (9.8 m/s2)(sin 40) = 6.3 m/s2. e) While the ball is in the air, its acceleration is 9.8 m/s2.

A steel ball is tied to the end of a string and swung in a vertical circle at constant speed. Complete the following statement: The direction of the acceleration of the ball is always a) perpendicular to the circle. b) toward the center of the circle. c) tangent to the circle. d) radially outward from the circle. e) vertically downward.

A steel ball is tied to the end of a string and swung in a vertical circle at constant speed. Complete the following statement: The direction of the acceleration of the ball is always a) perpendicular to the circle. b) toward the center of the circle. c) tangent to the circle. d) radially outward from the circle. e) vertically downward.

A steel ball is tied to the end of a string and swung in a vertical circle at constant speed. Complete the following statement: The direction of the instantaneous velocity of the ball is always a) perpendicular to the circle. b) toward the center of the circle. c) tangent to the circle. d) radially outward from the circle. e) vertically downward.

A steel ball is tied to the end of a string and swung in a vertical circle at constant speed. Complete the following statement: The direction of the instantaneous velocity of the ball is always a) perpendicular to the circle. b) toward the center of the circle. c) tangent to the circle. d) radially outward from the circle. e) vertically downward.

A bicycle racer is traveling at constant speed v around a circular track. The centripetal acceleration of the bicycle is ac. What happens to the centripetal acceleration of the bicycle if the speed is doubled to 2v? a) The centripetal acceleration increases to 4ac. b) The centripetal acceleration decreases to 0.25 ac. c) The centripetal acceleration increases to 2ac. d) The centripetal acceleration decreases to 0.5ac. e) The centripetal acceleration does not change.

A bicycle racer is traveling at constant speed v around a circular track. The centripetal acceleration of the bicycle is ac. What happens to the centripetal acceleration of the bicycle if the speed is doubled to 2v? a) The centripetal acceleration increases to 4ac. b) The centripetal acceleration decreases to 0.25 ac. c) The centripetal acceleration increases to 2ac. d) The centripetal acceleration decreases to 0.5ac. e) The centripetal acceleration does not change.

4. 7. 4. A satellite orbits the Earth in uniform circular motion
A satellite orbits the Earth in uniform circular motion. What is the direction of centripetal acceleration of the satellite? a) The centripetal acceleration is a scalar quantity and it doesn’t have a direction. b) The centripetal acceleration vector points radially outward from the Earth. c) The centripetal acceleration vector points radially inward toward the Earth. d) The centripetal acceleration vector points in the direction of the satellite’s velocity. e) The centripetal acceleration vector points in the direction opposite that of the satellite’s velocity.

4. 7. 4. A satellite orbits the Earth in uniform circular motion
A satellite orbits the Earth in uniform circular motion. What is the direction of centripetal acceleration of the satellite? a) The centripetal acceleration is a scalar quantity and it doesn’t have a direction. b) The centripetal acceleration vector points radially outward from the Earth. c) The centripetal acceleration vector points radially inward toward the Earth. d) The centripetal acceleration vector points in the direction of the satellite’s velocity. e) The centripetal acceleration vector points in the direction opposite that of the satellite’s velocity.

A motorcycle travels at a constant speed around a circular track. Which one of the following statements about this motorcycle is true? a) The car has a velocity vector that points along the radius of the circle. b) The car is characterized by constant velocity. c) The car is characterized by constant acceleration. d) The velocity of the car is changing. e) The car has an acceleration vector that is tangent to the circle at all times.

A motorcycle travels at a constant speed around a circular track. Which one of the following statements about this motorcycle is true? a) The car has a velocity vector that points along the radius of the circle. b) The car is characterized by constant velocity. c) The car is characterized by constant acceleration. d) The velocity of the car is changing. e) The car has an acceleration vector that is tangent to the circle at all times.

4. 7. 6. A truck is traveling with a constant speed of 15 m/s
A truck is traveling with a constant speed of 15 m/s. When the truck follows a curve in the road, its centripetal acceleration is 4.0 m/s2. What is the radius of the curve? a) 3.8 m b) 14 m c) 56 m d) 120 m e) 210 m

4. 7. 6. A truck is traveling with a constant speed of 15 m/s
A truck is traveling with a constant speed of 15 m/s. When the truck follows a curve in the road, its centripetal acceleration is 4.0 m/s2. What is the radius of the curve? a) 3.8 m b) 14 m c) 56 m d) 120 m e) 210 m

If an object is moving in uniform circular motion, its period is given by which one of the following quantities? a) the speed of the object b) the centripetal acceleration of the object c) the number of revolutions the object makes each second d) the time interval for the object to make one revolution e) the displacement of the object

If an object is moving in uniform circular motion, its period is given by which one of the following quantities? a) the speed of the object b) the centripetal acceleration of the object c) the number of revolutions the object makes each second d) the time interval for the object to make one revolution e) the displacement of the object

4.7.8. When using the term “uniform circular motion,” what do we mean by the term “uniform?”
a) The direction of the object’s velocity is constant. b) The net force on the moving object is zero newtons. c) The forces acting on the object are uniformly applied from all directions. d) The motion occurs without the influence of the gravitational force. e) The motion of the object is at a constant speed.

4.7.8. When using the term “uniform circular motion,” what do we mean by the term “uniform?”
a) The direction of the object’s velocity is constant. b) The net force on the moving object is zero newtons. c) The forces acting on the object are uniformly applied from all directions. d) The motion occurs without the influence of the gravitational force. e) The motion of the object is at a constant speed.

4.7.9. For an object in uniform circular motion, which of the following statements is false ?
a) The velocity of the object is constant. b) The magnitude of the acceleration of the object is constant. c) The acceleration is directed radially inward. d) The magnitude of the velocity is constant. e) The velocity is directed in a direction that is tangent to the circular path.

4.7.9. For an object in uniform circular motion, which of the following statements is false ?
a) The velocity of the object is constant. b) The magnitude of the acceleration of the object is constant. c) The acceleration is directed radially inward. d) The magnitude of the velocity is constant. e) The velocity is directed in a direction that is tangent to the circular path.

At one point during the Tour de France bicycle race, three racers are riding along a straight, level section of road. The velocity of racer A relative to racer B is ; the velocity of A relative to C is ; and the velocity of C relative to B is If = +6.0 m/s, and = +2.0 m/s, what is ? a) m/s b) m/s c) m/s d) 4.0 m/s e) 2.0 m/s

At one point during the Tour de France bicycle race, three racers are riding along a straight, level section of road. The velocity of racer A relative to racer B is ; the velocity of A relative to C is ; and the velocity of C relative to B is If = +6.0 m/s, and = +2.0 m/s, what is ? a) m/s b) m/s c) m/s d) 4.0 m/s e) 2.0 m/s

Reference frame A is in motion with respect to reference frame B. Complete the following statement: The speed of an object with respect to reference frame A a) must be equal to the speed of the object with respect to reference frame B. b) must be less the speed of the object with respect to reference frame B. c) must be greater than the speed of the object with respect to reference frame B. d) may or may not be equal to the speed of the object with respect to reference frame B. e) cannot be equal to the speed of the object with respect to reference frame B.

Reference frame A is in motion with respect to reference frame B. Complete the following statement: The speed of an object with respect to reference frame A a) must be equal to the speed of the object with respect to reference frame B. b) must be less the speed of the object with respect to reference frame B. c) must be greater than the speed of the object with respect to reference frame B. d) may or may not be equal to the speed of the object with respect to reference frame B. e) cannot be equal to the speed of the object with respect to reference frame B.

Reference frame A is in motion with respect to reference frame B. Complete the following statement: The velocity of an object with respect to reference frame A a) must be equal to the speed of the object with respect to reference frame B. b) must be less the speed of the object with respect to reference frame B. c) must be greater than the speed of the object with respect to reference frame B. d) may or may not be equal to the speed of the object with respect to reference frame B. e) cannot be equal to the speed of the object with respect to reference frame B.

Reference frame A is in motion with respect to reference frame B. Complete the following statement: The velocity of an object with respect to reference frame A a) must be equal to the speed of the object with respect to reference frame B. b) must be less the speed of the object with respect to reference frame B. c) must be greater than the speed of the object with respect to reference frame B. d) may or may not be equal to the speed of the object with respect to reference frame B. e) cannot be equal to the speed of the object with respect to reference frame B.

4. 9. 1. Two private airplanes are taxiing at a small airport
Two private airplanes are taxiing at a small airport. Jim is in plane A rolling due south with respect to the ground. Samantha is in plane B rolling due west with respect to the ground. Samantha is in front of Jim and to his left. In what direction(s), relative to himself, does Jim see Samantha’s plane moving? a) due east b) due west c) due south d) to the south and to the east e) to the north and to the west

4. 9. 1. Two private airplanes are taxiing at a small airport
Two private airplanes are taxiing at a small airport. Jim is in plane A rolling due south with respect to the ground. Samantha is in plane B rolling due west with respect to the ground. Samantha is in front of Jim and to his left. In what direction(s), relative to himself, does Jim see Samantha’s plane moving? a) due east b) due west c) due south d) to the south and to the east e) to the north and to the west

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