Question

A pellet (20g) is launched horizontally off a cliff (20m high) from a spring-loaded gun. The spring has constan k=1800 N/m and is compressed 0.10m before launch.

How much kinetic energy does the pellet have just before it hits the ground?
How fast will the pellet be going just before it hits the ground?

The spring is compressed twice as much for a second firing.
How fast will the pellet be moving just after launch? How far will it go horizontally before it hits the ground?

Answer 1

KE=spring PE+gravitational PE
KE=1/2 k x^2+ m*g*20m
at ground level,
1/2 m vf^2=1/2 k x^2 + 20mg
solve for vf.

b. if compressed twice as much, the spring has 4x as much PE,
find the time to fall 20m
20=1/2 g t^2 solve for time t.
then, how far horizontal=20t

Answer 2

Do the m and 1/2 cancel each other out for the ground level question?

Answer 3

NO. They don't cancel. But they're given.