Water slides and speeds

Question

There is a waterslide that has a height of 51.38 meters and the top of the hill is 17 meters.

 

a) assuming frictionless track, determine the maximum speed of the raft.

 

b) what locations does the raft reach this speed?

 

c) how fast is the raft moving when it reaches the top of the 17 meter hill?

Answer 1

Use energy conservation: K_i + U_i = K_f + U_f

 

a) At the top of the waterslide, K_i = 0.  The maximum speed occurs when h_f = 0, so U_f = 0.

 

U_i = K_f

 

mgh_i = ½mv_f²

 

v_f = √(2gh_i) = √(2·9.8·51.38) =  31.7 m/s

 

 

b) The maximum speed is reached at the bottom of the waterslide.

 

 

c) K_i = 0 at the top of the waterslide.  h_f = 17 m.

 

U_i = K_f + U_f

 

mgh_i = ½mv_f² + mgh_f

 

v_f = √[2g(h_i - h_f)] = 26.0 m/s