PROJECTILE MOTION

Relevant Physics: The Independence of the Vertical and Horizontal directions means that a projectile motion problem consists of two independent parts: The path of any projectile is a parabola Vertical motion at a constant downward acceleration, which is equal to a = -g = -9.80 m/s2. Horizontal motion at a constant horizontal speed, vx = constant.

The object's vertical motion is the same as that of an object undergoing only vertical free-fall. Gravity only affects the object's vertical motion. Gravity cannot change the object's horizontal speed, and the component of the object's horizontal velocity remains constant throughout its motion.

Information Implied: We neglect any effects due to air resistance on the object. We neglect any effects due to the Earth's rotation. The object does not rise high enough for the acceleration of gravity to change -- the body's acceleration is assumed to be both constant and downward regardless of its direction of motion or its height above the ground. The time of rise to its highest point is equal to the time of fall from its highest point back to the ground. The vertical component of velocity is zero at its highest point. The horizontal velocity remains constant through out its flight. The magnitude of the objects velocity when the object hits the ground is the same as its initial launch velocity. The only difference is that its angle relative to horizontal when it hits the ground is now the negative of the object's launch angle

Frame of Reference: * Projectile motion problems need a two dimensional coordinate system to describe the projectile's motion. The y-direction is usually associated with the vertical motion and location of the projectile, while the x-direction is usually associated with the horizontal motion and location of the projectile.* The generic equations for projectile motion assume the origin is at ground level, up is positive, right is positive, and that the clock starts the moment the projectile leaves the ground.

ay = -g Vertical Motion: Constant Downward Acceleration Vy = Vyo – gt Y = Vyot – 1/2gt2 Vy2 = V2yo – 2gy Vyo = VosinQ

ax = 0 Constant Horizontal Speed Horizontal Motion: ax = 0 Constant Horizontal Speed Vx = Vxo X = Vxot Vx = VocosQ X = V2osin2Q/g

Total Space Motion: a = g

PROJECTILE MOTION PROBLEM SOLVING The vertical and horizontal motions of any projectile are independent of each other. This means that any projectile problem can be resolved into two problems - a vertical problem and a horizontal problem that can be solved independent of each other. This also means that one must be able to resolve the velocity vector into horizontal and vertical components at any point in the projectiles trajectory or its opposite, combine the horizontal and vertical components at any moment to find the projectile’s speed and direction

RELEVANT PROJECTILE QUESTIONS: What is the half time of flight? What is the total time of flight? What is the height of the trajectory? What is the range of the trajectory? What is the vector displacement at a certain time? What is the vector velocity at a certain time?

Question 1. 1. A ball is launched into the air at an angle of 32 Question 1. 1. A ball is launched into the air at an angle of 32.00 with an initial speed of 18.0 m/s. Neglecting air resistance, determine how long the ball will be in the air ?

Question 2. A rock is launched from the ground into the air. After 1 Question 2. A rock is launched from the ground into the air. After 1.40 seconds the rock is observed to have a speed of 22.0 m/s at an angle +18.0o above horizontal. Neglecting air resistance, with what speed was the rock launched ?

Question 3. A ball is tossed into the air at a speed of 64 Question 3. A ball is tossed into the air at a speed of 64.0 m/s at an unknown angle. If the ball is observed to rise to a maximum height of 7.80 m, at what angle was the ball thrown relative to the ground ?

Question 4. An object is launched from the ground into the air at an angle of 38.0o (above the horizon) towards a vertical brick wall that is 15.0 m horizontally from the launch point. If the ball takes 1.30 seconds to collide with the wall, with what speed was the ball launched ?

Problem 5: A kicker punts a football from a height of 1 m at 20m/s at an angle of 37 degrees. Find the distance the ball traveled Before hitting the ground.

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