A child of mass m = 28 kg slides down a slide of height h = 2.1 m without friction. Let gravitational potential energy be zero at ground level.

Question

Write an expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g. 

Calculate the change in the child's potential energy, ΔU in joules, from the top to the bottom of the slide at ground level (i.e. ΔU = U_ground - U_top). 

What is the child's final speed, v_f in m/s? 

Answer 1

E = mv²/2 + mgh = 0 + mgh = mgh

m = 28 kg

g = 9.8 m/s²

h = 2.1 m

Plug in the numbers and get E in joules.

ΔU = mg(0) - mgh = -mgh

Plug in the numbers and get ΔU in joules.

mv_f²/2 = mgh

v_f = √(2gh)

Plug in the numbers and get v_f in m/s.