Solutions must be worked out symbolically first (that is, in terms of variables

Question

Solutions must be worked out symbolically first (that is, in terms of variables and constants) with numbers plugged in as the very last step. Make sure to double check the answer!

A rifle is held horizontally and aimed directly at the bullseye on a target 200m away. When it leaves the muzzle, the bullet is traveling at 500m/s. How far below the bullseye does the bullet hit?

A ball rolls straight off of a table with a horizontal speed of 1.25m/s. The table is 0.9 m tall. How much time does it take the ball to reach the floor? How far from the table does it land? What is the ball’s velocity when it lands?

Explanation / Answer

part a)

The x component of the velocity won't change until it hits the target.

However, gravity will be pushing the bullet down for as long as it is travelling.

If I use t= (d/v) then that means t=(200m/500m/s) so t=0.40s So if acceleration is 9.8 m/s per second, multiplied by 0.40s would mean the bullet dropped 3.92m.

part b)

h = 0.5gt^2

or, 0.9 = 0.5x9.8xt^2

or, t = 0.428 s

How far from the table does it land:

d = vt = 1.25x0.428 = 0.535 m

What is the ball’s velocity when it lands:

v = u + gt = 1.25 + 9.8x0.428 = 5.44 m/s

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