TDK - Projectile Motion

Projectile Motion

Projectile motion involves objects that are traveling through the air under the influence of gravity. No other acceleration is present. To solve projectile motion problems it is necessary to treat the x and y axis separately. Given quantities are separated into their x and y components. In the y axis any appropriate kinematic equation can then be applied to solve for the five different variables. In the x axis there is no acceleration so the only equation available is for constant velocity. Once variables have been solved for in each axis, the x and y components can be resolved to calculate the correct answer. The only variable whose value applies to both axes is time. It is very important that if the answer to a problem requires a vector as the answer that both the magnitude and direction be given. Please watch this presentation on projectile motion.

Projectile Motion Practice

The following presentation will give you some examples of problems using projectile motion.

Projectile Motion Self-Assessment

Now it is your turn. Complete the self-check questions to verify that you understand how to solve problems dealing with objects moving in one dimension under constant acceleration.

  1. A 4 m long cannon shoots a cannon ball. The cannon ball accelerates from rest at 50 m/s2  until it exits the cannon. For this problem, the cannon is angled at 35 degrees to the horizontal.
    1. What is the velocity (magnitude and direction) of the cannon ball as it exits the cannon?
    2. How high is it above the ground when it exits?
    3. What is the maximum height reached by the cannon ball?
    4. What is the velocity of the cannon ball at the maximum height?
    5. How long is the cannon ball in the air?
    6. What is the horizontal displacement of the cannon ball?
    7. What is the final velocity of the cannon ball?
    8. Draw a graph of the velocity of the cannon ball from the moment it leaves the cannon until the instant it hits the ground. 

SOLUTIONS Links to an external site.

 

  1. A little girl is out kicking her soccer ball. She stands 25 m from a soccer goal that 2.6 m tall. She kicks a soccer ball with an initial velocity of 32 m/s at 47 degrees. 
    1. How long does it take to get to the soccer goal?
    2. As it passes the soccer goal cross bar, is it above the bar, below the bar, or does it hit the bar?   If it misses, how much does it miss by?
    3. Was the ball on the way down, or going up as it passed the cross bar?
    4. Draw a graph of the acceleration of the soccer ball as a function of time.
    5. What was the displacement of the soccer ball from the time it left the girl's feet until it passed the cross bar? 

SOLUTIONS Links to an external site.

 

  1. A helicopter is flying at 200 m above the ground. It intends to drop a package to a village. At the moment the package is dropped the helicopter is flying 53.3 m/s at 21 degrees.
    1. How long will it take the package to hit the ground?
    2. How far horizontally from the drop zone should the helicopter be when the package is released?
    3. What will be velocity of the package as it hits the ground? 

SOLUTIONS Links to an external site.

Projectile Motion Practice Problems

Download Projectile Motion Practice Problems Links to an external site..

Download solutions Links to an external site. for the practice problems. 

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