A helicopter is traveling at 40 m/s at a constant altitude of 100 m over a level field. If a wheel falls off the helicopter, with what velocity will it hit the ground? (g = 9.8 m/s2 and air resistance negligible) 40 m/s 50 m/s 60 m/s 70 m/s 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A stone is thrown horizontally from the top edge of a cliff with an initial speed of 10 m/s. A stop watch measures the stone's trajectory time from top of cliff to bottom to be 4.3 s. What is the height of the cliff? (g = 9.8 m/s2 and air resistance is negligible) 22 m 43 m 77 m 91 m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A stone is thrown horizontally from the top edge of a cliff with an initial speed of 10 m/s. A stop watch measures the stone's trajectory time from top of cliff to bottom to be 4.3 s. How far out from the cliff's edge does the stone travel horizontally? (g = 9.8 m/s2 and air resistance is negligible) 22 m 43 m 77 m 91 m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

just after leaving centerfielder's hand A baseball is thrown by the centerfielder (from shoulder level) to home plate where it is caught (on the fly at shoulder level) by the catcher. At what point does the magnitude of the vertical component of velocity have its minimum value? (air resistance is negligible) just after leaving centerfielder's hand just before arriving at catcher's mitt at the top of the trajectory magnitude of vertical component of velocity is constant 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

just after leaving the centerfielder's hand A baseball is thrown by the centerfielder (from shoulder level) to home plate where it is caught (on the fly at shoulder level) by the catcher. At what point is the ball's speed at a minimum? (air resistance is negligible) just after leaving the centerfielder's hand just before arriving at the catcher's mitt at the top of the trajectory speed is constant during entire trajectory 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

just after leaving centerfielder's hand A baseball is thrown by the centerfielder (from shoulder level) to home plate where it is caught (on the fly at shoulder level) by the catcher. At what point is the magnitude of the acceleration at a minimum? (air resistance is negligible) just after leaving centerfielder's hand just before arriving at catcher's mitt at the top of the trajectory acceleration is constant during entire trajectory 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.4 m/s at an initial angle of 30° with respect to the horizontal. What is the maximum vertical displacement that the ball reaches during its trajectory? 11.0 m 9.8 m 22.1 m 44.1 m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Five boys are pushing on a snowball, and each is pushing with a force of 10.0 N. However, each boy is pushing in a different direction. They are pushing north, northeast, east, southeast, and south. (Each boy is pushing at an angle of 45° relative to his neighbor.) What is the total push on the ball? 17.1 N 24.1 N 27.1 N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A baseball thrown from the outfield is thrown from shoulder height at an initial velocity of 29.4 m/s at an initial angle of 30° with respect to the horizontal. It is in its trajectory for a total interval of 3 s before it is caught by the third baseman at shoulder-height level. (Assume air resistance negligible.) What is the ball's horizontal displacement? 76.4 m 38.2 m 57.3 m zero 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A baseball thrown from the outfield is released from shoulder height at an initial velocity of 29.4 m/s at an initial angle of 30° with respect to the horizontal. If it is in its trajectory for a total of 3 s before being caught by the third baseman at shoulder-height level, what is the ball's net vertical displacement during its 3 s trajectory? 11.0 m 9.8 m 22.1 m zero 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

The first displacement is 6 m and the second displacement is 3 m The first displacement is 6 m and the second displacement is 3 m. They cannot add together to give a total displacement of 2 m 3 m 6 m 9 m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Vector A is 3 units in length and points along the positive x-axis; vector B is 4 units in length and points along a direction 150° from the positive x-axis. What is the magnitude of the resultant when vectors A and B are added? 7.0 6.7 4.7 2.1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Vector A is 3 units in length and points along the positive x-axis; vector B is 4 units in length and points along a direction 150° from the positive x-axis. What is the direction of the resultant with respect to the positive x-axis? 77° 13° 86° 103° 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

I walk six miles in a straight line in a direction north of east and I end up 2 miles east and several miles north. How many degrees north of east have I walked? 19° 45° 60° 71° 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A jogger runs halfway around a circular path with a radius of 60 m A jogger runs halfway around a circular path with a radius of 60 m. What, respectively, are the displacement and distance jogged? 60 m, 188 m 120 m, 188 m 0 m, 377 m 120 m, 377 m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Vector A points south and vector B points west Vector A points south and vector B points west. If we subtract A from B, the direction of the vector (B - A) points north of east south of east north of west south of west 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

59° N of E 29° N of E 29° N of W 77° N of E An ant on a picnic table travels 30 cm eastward, then 25 cm northward and finally 15 cm westward. What is its directional displacement with respect to its original position? 59° N of E 29° N of E 29° N of W 77° N of E 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A student adds two vectors with magnitudes of 200 and 40 A student adds two vectors with magnitudes of 200 and 40. Of the following, which one is the only possible choice for the magnitude of the resultant? 100 200 260 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A string attached to an airborne kite is maintained at an angle of 40° with the horizontal. If a total of 120 m of string is reeled in while bringing the kite back to the ground, what is the horizontal displacement of the kite in the process (assume the kite string doesn't sag)? 100 m 84 m 77 m 92 m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A boy pulls a sled across a level field by exerting a force of 110 N at an angle of 30° with the ground. What are the parallel and perpendicular components, respectively, of this force with respect to the ground? 64 N, 190 N 190 N, 64 N 95 N, 55 N 55 N, 95 N 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

An ant on a picnic table travels 30 cm eastward, then 25 cm northward and finally 15 cm westward. What is the magnitude of its net displacement? 70 cm 57 cm 52 cm 29 cm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Of the following, which type of quantity is characterized by both magnitude and direction? scalar vector trigonometric algebraic variable 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

cosine sine tangent cotangent In a 2-dimensional cartesian coordinate system the y-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function, with respect to the angle between vector and x-axis? cosine sine tangent cotangent 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

An example of a vector quantity is which of the following? velocity temperature volume mass 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

cosine sine tangent cotangent In a 2-dimensional cartesian coordinate system the x-component of a given vector is equal to that vector`s magnitude multiplied by which trigonometric function, with respect to the angle between vector and x-axis? cosine sine tangent cotangent 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

When one subtracts a velocity vector from another velocity vector, the result is which of the following? another velocity an acceleration a displacement a scalar 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

When one adds a displacement vector to another displacement vector, the result is which of the following? a velocity an acceleration another displacement a scalar 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A fireman, 50 m away from a burning building, directs a stream of water from a firehose at an angle of 30° above the horizontal. If the velocity of the stream is 40 m/s, at what height will the stream of water strike the building? 9.6 m 13.4 m 18.7 m 22.4 m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

1.8 minutes 2.4 minutes 3.0 minutes 1.3 minutes The highest mountain on Mars is Olympus Mons, rising 22,000 meters above the Martian surface. If we were to throw an object horizontally off the mountain top, how long would it take to reach the surface? (Ignore atmospheric drag forces and use gMars = 3.72 m/s 2 .) 1.8 minutes 2.4 minutes 3.0 minutes 1.3 minutes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Wiley Coyote has missed the elusive road runner once again Wiley Coyote has missed the elusive road runner once again. This time, he leaves the edge of the cliff at 50 m/s horizontal velocity. If the canyon is 100 m deep, how far from the edge of the cliff does the coyote land? 112 m 225 m 337 m 400 m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Superman is flying at treetop level near Paris when he sees the Eiffel Tower elevator start to fall (the cable snapped). His x-ray vision tells him Lois Lane is inside. If Superman is 1 km away from the tower, and the elevator falls from a height of 240 m, how long does Superman have to save Lois, and what must be his average velocity? 3 s, 333 m/s 5 s, 200 m/s 7 s, 143 m/s 9 s, 111 m/s 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

It is said that in his youth George Washington threw a silver dollar across a river. Assuming the river was 75 m wide and the coin was thrown at a 45° angle, what minimum initial speed was required to get the coin across the river? 7 m/s 14 m/s 21 m/s 28 m/s 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A baseball leaves the bat with a speed of 44 m/s and an angle of 30° above the horizontal. A 5 m high fence is located at a horizontal distance of 132 m from the point where the ball is struck. Assuming the ball leaves the bat 1 m above ground level, by how much does the ball clear the fence? 4.4 m 8.8 m 13.4 m 17.9 m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A river flows due east at 3 m/s A river flows due east at 3 m/s. A boat crosses the 300 m wide river by maintaining a constant velocity of 10 m/s due north relative to the water. If no correction is made for the current, how far downstream does the boat move by the time it reaches the far shore? 6 m 30 m 60 m 90 m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A track star in the broad jump goes into the jump at 12 m/s and launches himself at 20° above the horizontal. How long is he in the air before returning to Earth? (g = 9.8 m/s2 ). 0.42 s 0.83 s 1.25 s 1.66 s 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A jet airliner moving at 500 mph due east moves into a region where the wind is blowing at 120 mph in a direction 30° north of east. What is the new velocity and direction of the aircraft? 607 mph, 5.67° N of E 620 mph, 7.10° N of E 550 mph, 6.22° N of E 588 mph, 4.87° N of E 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A boat moves at 10 m/s relative to the water A boat moves at 10 m/s relative to the water. If the boat is in a river where the current is 2 m/s, how long does it take the boat to make a complete round trip of 1000 m upstream followed by a 1000 m trip downstream? 200 s 203 s 208 s 250 s 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

42.7 yards 55 yards 62.5 yards 75 yards A quarterback takes the ball from the line of scrimmage, runs backward for 10 yards, then sideways parallel to the line of scrimmage for 15 yards. He then throws a 50-yard forward pass straight downfield perpendicular to the line of scrimmage. The receiver is tackled immediately. How far is the football displaced from its original position? 42.7 yards 55 yards 62.5 yards 75 yards 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A stone is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal from the top of a 35 m building. If g = 9.8 m/s2 and air resistance is negligible, what is the magnitude of the horizontal displacement of the rock? 38 m 46 m 66 m 90 m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A bridge that was 5 m long has been washed out by the rain several days ago. How fast must a car be going to successfully jump the stream? Although the road is level on both sides of the bridge, the road on the far side is 2 m lower than the road on this side. 5 m/s 8 m/s 13 m/s 25 m/s 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A rifle is aimed horizontally toward the center of a target 100 m away A rifle is aimed horizontally toward the center of a target 100 m away. If the bullet strikes 10 cm below the center, what was the velocity of the bullet? (Ignore air friction.) 300 m/s 333 m/s 500 m/s 700 m/s 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A stone is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal from the top of a 35 m building. If g = 9.8 m/s2 and air resistance is negligible, then what is the speed of the rock as it hits the ground? 15 m/s 21 m/s 30 m/s 36 m/s 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A stone is thrown at an angle of 30° above the horizontal from the top edge of a cliff with an initial speed of 12 m/s. A stop watch measures the stone's trajectory time from top of cliff to bottom to be 5.6 s. How far out from the cliff's edge does the stone travel horizontally? (g = 9.8 m/s2 and air resistance is negligible) 58 m 154 m 120 m 197 m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A stone is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal from the top of a 35 m building. If g = 9.8 m/s2 and air resistance is negligible, then what is the magnitude of the vertical velocity component of the rock as it hits the ground? 9.0 m/s 18 m/s 26 m/s 29 m/s 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A stone is thrown with an initial speed of 15 m/s at an angle of 53° above the horizontal from the top of a 35 m building. If g = 9.8 m/s2 and air resistance is negligible, then what is the magnitude of the horizontal component of velocity as the rock strikes the ground? 7.5 m/s 9.0 m/s 12 m/s 29 m/s 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A stone is thrown at an angle of 30° above the horizontal from the top edge of a cliff with an initial speed of 12 m/s. A stop watch measures the stone's trajectory time from top of cliff to bottom to be 5.6 s. What is the height of the cliff? (g = 9.8 m/s2 and air resistance is negligible) 58 m 154 m 120 m 197 m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

dividing by cosine dividing by sine multiplying by cosine In a 2-dimensional cartesian system, if the x-component of a vector is known, as well as the angle between vector and x-axis, then the magnitude of the vector is calculated by which operation, taken with respect to the x-component? dividing by cosine dividing by sine multiplying by cosine multiplying by sine 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

14.0 blocks 8.4 blocks 11.1 blocks 13.0 blocks A city jogger runs ten blocks due east, five blocks due south and another two blocks due east. Assume all blocks are of equal size. What is the magnitude of the jogger's displacement, start to finish? 14.0 blocks 8.4 blocks 11.1 blocks 13.0 blocks 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

75.0 newtons 7.5° 61.4 newtons 21.8° 23.4 newtons 18.3° The following force vectors act on an object: i) 50 newtons at 45° north of east and ii) 25 newtons at 30° south of east. Which of the following represents the magnitude of the resultant and its angle relative to the easterly direction? 75.0 newtons 7.5° 61.4 newtons 21.8° 23.4 newtons 18.3° 12.8 newtons 37.5° 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Find the resultant of the following two vectors: i) 200 units due east and ii) 400 units 30° north of west. 300 units 30° north of west 616 units 15° north of west 546 units 60° north of west 248 units 54° north of west 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50