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Objective:
By the end of this module you should be able to:
- Recognize that projectile motion can be analyzed by considering the horizontal and vertical components of the motion separately.
- Apply kinematic equations for constant velocity to analyze the horizontal motion of a projectile.
- Apply kinematic equations for uniform acceleration to analyze the vertical motion of a projectile.
- Solve a variety of problems related to projectile motion.
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Introduction:
In the last module we looked at the theory relating to projectile motion. The main points that you need to remember are:
- An object in free fall will accelerate at 9.81 meters per second squared downwards.
- When investigating the trajectory of a projectile we can look at the horizontal motion and the vertical motion separately.
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- In the horizontal direction, there are no external forces. Therefore, there is no acceleration. Velocity in the horizontal direction is constant. We can see this in the diagram because all horizontal velocity vectors are the same magnitude.
- In the vertical direction, the only force acting on the projectile is gravity. Therefore the object will accelerate at a rate of 9.81 meters per second squared downwards. Again, we see this is the diagram at the right. The vertical velocity vectors increase in magnitude as the projectile continues to move along its trajectory.
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- And if a projectile is launched horizontal, then there is no initial velocity in the vertical direction. There is only an initial velocity in the horizontal direction.
Using our 3 main kinematic equations, we will now be using the following equations. Instead of using d for displacement we will use x for displacement in the horizontal direction and y for displacement in the vertical direction. And most importantly: DO NOT MIX VELOCITIES. vi in the horizontal direction can not be substituted in for vi in the vertical direction. The only variable that can be used in both directions is t, time.
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In the horizontal direction:
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In the vertical direction:
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Example:
A ball rolls off of a table with a speed of 3.2 m/s. The table is 1.5 m high.
a) When does the ball hit the ground?
b) How far away from the base of the table does the ball travel?
c) With what speed does the ball hit the floor?
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Activities:
Read the following links:
Take notes as you read through the sections.
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Practice:
Answer the following questions. The solutions are given below, but make a fair attempt to do these questions on your own. If you are having difficulty or do not understand the solution you can either e-mail your "homework buddy" or myself.
- A stone is thrown horizontally at a speed of 5.0 m/s from the top of a cliff 78.4 m high. a) How long does it take the stone to reach the bottom of the cliff? b) How far from the base of the cliff does the stone strike the ground? c) What are the horizontal and vertical components of the velocity of the stone as it hits the ground? d) What is the final speed of the stone as it hits the ground?
- How would the answers to a), b) and c) of question 1 change if a) the stone were thrown with twice the horizontal speed, or b) the stone were thrown with the same speed but the cliff were twice as high?
- A steel ball rolls with constant velocity on a tabletop 0.950 m high. It rolls off and hits the ground +0.352 m from the edge of the table. How fast was the ball rolling?
- A beach ball, moving with a speed of +1.27 m/s, rolls off a pier and hits the water 0.75 m from the end of the pier. How high is the pier above the water?
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