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## Homework Statement

A toy rocket that weighs 10 N blasts straight up from ground level with an initial kinetic energy of 40J. At the exact top of its trajectory, its total mechanical energy is 140J. To what vertical height above the ground does it rise, assuming no air resistance?

**2a. Relevant equations**

gravitational potential energy = mgh

potential + kinetic = mechanical energy

**3a. The attempt at a solution**

if the rocket has 40J of energy on the ground, it has gained 100J at the top of its trajectory*.

GPE = 100J

GPE = mgh

100 = (10)h

h = 10 meters

*I think this is true, but I can't explain why. It's not like it lost 40J of energy to reach the top, but if it's at the top, it isn't moving anymore, so the final kinetic energy is zero, yes?

also, is there a way to use kinematic equations to solve this problem? here's what I tried:

**2b. Relevant equations**

gravitational potential energy = mgh

potential + kinetic = mechanical energy

kinetic energy = 1/2mv^2

weight = mass * gravity

v(final)^2 = v(initial)^2 + 2ad

**3b. The attempt at a solution**

10N = m(10); m = 1kg

initial kinetic energy = 40J

40 = 1/2 m v^2; initial v^2 = 80

final velocity = 0

0 = 80 + 2(-10)d

d = 4 meters

I feel like I'm missing something fairly obvious. Thanks for any light you can shed.