What speed will the child reach the bottom of the slide

Question

A 42 kg child slides from the top of a 3 m high playground slide. With what speed will the child reach the bottom of the slide assuming: (a)There is no friction? (b) 23 J of energy is dissipated due to friction?

Answer 1

(a)

 

Use energy conservation.

 

mgh = mv²/2 ⇒

 

v = √(2gh) = √[2(9.8)(3)] m/s ≅ 7.67 m/s 

 

(b)

 

mv²/2 = mgh - (23 J) ⇒

 

v = √{(2/m)[mgh - (23 J)]} = √{(2/42)[42(9.8)(3) - 23]} m/s = 7.60 m/s