Conceptual Physics

4.4 - Sample problem: a horizontal cannon

Variables

What is the strategy?

1. Calculate how long the cannonball remains in the air. This can be done with a standard motion equation.


2. Use the elapsed time and the specified horizontal displacement to calculate the required horizontal firing velocity.

Physics principles and equations

The amount of time the ball takes to fall is independent of its horizontal velocity.

Step-by-step solution

We start by determining how long the cannonball is in the air. We can use a linear motion equation to find the time it takes the cannonball to
drop to the ground.

Now that we know the time the cannonball takes to fall to the ground, we can calculate the required horizontal velocity.

What horizontal firing (muzzle)

velocity splashes the cannonball into

the pond?

vertical displacement ǻy = í40.0 m

vertical acceleration ay = í9.80 m/s^2

horizontal displacement ǻx = 95.0 m

elapsed time t

horizontal velocity vx

Step Reason

1. ǻy = vyit + ½ ayt^2 linear motion equation

2. ǻy = (0)t + ½ ayt^2 initial vertical velocity zero

3. solve for time

4. enter values

5. t = 2.86 s evaluate

Step Reason

6. definition of velocity

7. enter values

8. vx = 33.2 m/s divide

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