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## Homework Statement

5. A 40 kg child jumps onto a playgorund slide at 3 m/s. If she slides down a vertical drop of 5.0 m while traveling 8.0 horizontally, find:

a) The speed of hte child at the bottom of the slide, if there is no friction.

b) The intial total energy of the child, relative to the bottom of the slide.

c) The amount of heat energy that must be generated if the child reaches speeds of 4.0 m/s at the bottom of the slide.

## Homework Equations

Epi + Eki = Epf + Ekf

P=mgh

K=(1/2)m(v^2)

## The Attempt at a Solution

a) The speed of the child at the bottom of the slide, if there is no friction.

Epi + Eki = Epf + Ekf

mgh + 0 = 0 + (1/2)m(v^2)

sqrt(2mgh/m) = v

sqrt(2gh) = v

sqrt(2*9.80*5.0) = v

sqrt(98) = v

v = 9.9 m/s?

b) The initial total energy of the child, relative to the bottom of the slide.

This one is confusing...

Epi = mgh

= 40kg * 9.80 * 5.0

= 90 J?

c) The amount of heat energy that must be generated if the child reaches speeds of 4.0 m/s at the bottom of the slide.

Heat = W = Fd = Delta Ke

Heat = Fd = (40*9.80)*(sqrt(25+64

Heat = Fd = (40*9.80)*(sqrt(89))

=400*9.4

= 4000 J?