Question

A 1500-kg car starts from rest at the top of a driveway 6.61 m long that is sloped at an angle of 20 degrees with the horizontal. If an average friction force of 3340 N impedes the motion of the car, find the speed (in m/s) of the car at the bottom of the driveway.

Answer 1

Answer:

7.77114 m/s

Explanation:

m = Mass of the car = 1500 kg

g = Acceleration due to gravity = 9.81 m/s²

h = Height of the driveway = 6.61 m

$\theta$ = Angle = 30°

f = Frictional force = 3340 N

The potential energy will balance the kinetic energy of the car

$mghsin\theta-f=\dfrac{1}{2}mv^2\\\Rightarrow v=\sqrt{\dfrac{2(mghsin\theta-f)}{m}}\\\Rightarrow v=\sqrt{\dfrac{2(1500\times 9.81\times 6.61\times sin30-3340)}{1500}}\\\Rightarrow v=7.77114\ m/s$

The speed of the car at the bottom of the driveway is 7.77114 m/s