Question

A roller coaster starts from rest at its highest point and then descends on its (frictionless) track. Its speed is 36 m/s when it reaches ground level. What was its speed when its height was half that of its starting point?

Answer 1

Answer:

its speed when its height was half that of its starting point is 25.46 m/s

Explanation:

Given;

final speed of the roller coaster, v = 36 m/s

Applying general equation of motion;

V² = U² + 2gh

where;

V is the final speed of the roller coaster

U is the initial speed of the roller coaster = 0

h is the height attained at a given velocity

36² = 0 + (2 x 9.8)h

1296 = 19.6 h

h = 1296/19.6

h = 66.1224 m

when its height was half that of its starting point, h₂ = ¹/₂ h

h₂ = ¹/₂(66.1224 m) = 33.061 m

At h = 33.061 m, V = ?

V² = U² + 2gh

V² = 0 + 2 x 9.8 x 33.061

V² = 648

V = √648

V = 25.46 m/s

Therefore, its speed when its height was half that of its starting point is 25.46 m/s