Question

A single roller-coaster car is moving with speed v0 on the first section of track when it descends a 4.7-m-deep valley, then climbs to the top of a hill that is 5.4 m above the first section of track. Assume any effects of friction or of air resistance are negligible.
(a) What is the minimum speed v0 required if the car is to travel beyond the top of the hill?
(b) Can we affect this speed by changing the depth of the valley to make the coaster pick up more speed at the bottom?

Answer 1

Explanation:

From the curve given in the attachment,

a) minimum speed v0 required if the car is to travel beyond the top of the hill

climb to the top = 5.4 m

Therefore, $V_0=\sqrt{2gh}$

$V_0=\sqrt{2(9.81)(5.4)}$ =  10.29 m/s

b) No, we cannot affect this speed by changing the depth of the valley to make the coaster pick up more speed at the bottom as this speed does not depend upon depth of the valley.