Question

A car turns into a driveway that slopes upward at a 9.0 ∘∘ angle. The car is moving at 7.3 m/sm/s .

Part A:

If the driver lets the car coast, how far along the slope will the car roll before being instantaneously at rest and then starting to roll back?

Express your answer to two significant figures and include the appropriate units.

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the car = m

Initial speed of the car = V = 7.3 m/s

Angle of the slope of the driveway = = 9^o

Distance the car will travel along the slope before coming to rest = L

Height gained by the car = H

H = LSin

The initial kinetic energy of the car is converted into the potential energy of the car as it goes up the slope.

mV²/2 = mgH

V²/2 = gLSin

L = 17 m

A) Distance the car will coast along the slope before coming to rest = 17 m