Unit 5 - Projectile Motion

Projectile Motion

Formulas:

From Miranda's yellow sheet:

• If an object is going down, the velocity and displacement are negative
• In the hypothetical situation of a ball being thrown into the air and caught in the same spot, the displacement is 0
• The acceleration is -10m/s^2 in the vertical direction for the object.  The horizontal direction does not have an acceleration, it has constant velocity.  
• Remember to differentiate the horizontal components from the vertical components (Vx and Viy)
• Horizontal velocity = Vx
• Vertical velocity = Viy
• The initial Viy is usually 0 (especially in the scenario of dropping something)
• When given the initial velocity with an angle, make sure to solve for the Vx and the Viy.  DO NOT use the velocity given to you.

To not get confused with your components, try writing out one of these charts on the side of your problems to differentiate where each piece of information goes.

This is what a motion map for an object falling off of a table would look like.  Notice the X and Y components along with the actual movement of the object (in red).

Practice problems!!

1. A ball is thrown downward with an initial speed of 20m/s.  What's the ball's acceleration?  Calculate the displacement during the first 4 seconds.  Then, calculate the time it takes to reach a speed of 50 m/s, and how long it would take to fall 300 meters.

a = -10m/s^2

First, solve for the displacement by plugging in 4 for time.

 Then, Use the Vf that you were given to solve for the time.  Remember that the final velocity is negative because the object is going downward.

To solve for the amount of time it would take to reach 300m, plug in -300 meters as the change in x, and transform the problem into an ax^2 + bx + c formula (to use the quadratic formula).  

2. A student finds that it takes 0.2 seconds for a ball to pass through photo gates placed 30 cm apart on a level ramp.  The end of the ramp is 92 cm above the floor.  Where can we place a coin to ensure that the ball will land on top of the coin?

 Solve for the time by plugging in -.92 as the displacement (remember, negative because it's going down)

 Then, use the information you know (displacement in the x direction and the time) to solve for the velocity in the x direction.

Once you have found the velocity in the x direction, use it and the time to solve for the displacement in the x direction.  This tells you how far away you should place the coin.

3. A kickoff sends a football with an initial velocity of 25m/s at an angle of 50 degrees above the horizontal.  Find the x and y components of the velocity, the time the ball is in the air, and the horizontal distance the ball travels before it hits the ground.  

First, solve for the X and Y components.  You don't want to use the velocity that the problem gave you.

Then, plug the Viy that you solved for into the displacement equation, using 0 as the displacement in the y direction.  You use 0 as the displacement in this case because the ball did not change it's position in the y direction, it landed at the exact same height that it started at.  Solve for the time with this information.

Solve for the displacement in the x direction by plugging in the x velocity you solved for, and the time you solved for in the previous step. 

4. A water balloon is launched at a building 24 meters away with an initial velocity of 18m/s at an angle of 50 degrees above the horizontal.  At what height will the balloon strike the building?

First, split the velocity that you are given into X and Y components. 

 You now have to find the time.  You are not given the displacement in the y direction, so you must use another formula.  You know that the displacement in the x direction is 24, and you just solved for the Vx, so plug those into the corresponding formula and solve for the time.

Once you have solved for time, you can solve for the displacement in the y direction.