A car is parked on a cliff overlooking the ocean on an incline that makes an ang

Question

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 18? below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 3.2 m/s2 and travels 42 m to the edge of
the cliff. The cliff is 35 m above the ocean. The acceleration of gravity is 9.81 m/s2 . ~How long is the car in the air? Answer in units of s. Do not round off any numbers during calculations and in the problem.

~What is the car's position relative to the base of the cliff when the car lands in the ocean? Answer in units of m. Do not round off any numbers during calculations and in the problem.

Explanation / Answer

constant acceleration of car is a = 3.2 m/s2 The height of the cliff is h = 35 m The distance of the car travelled is x = 42 m
The equations of the motion of car are:
Horizontal motion
v^2=u^2+2as
where u=0, a=3.2 m/s^2 and s=42 m.
so v= 16.395121225535357413153661888834 m/s
vertical motion
we get
h=ut+1/2*gt^2
35 m =16.395121225535357413153661888834sin(18)t+0.5*9.8*t^2
t = 2.2051772836374725 s
use t with equation
x=v.sin(theta)t
=16.395121225535357413153661888834 cos(18)*2.2051772836374725
=34.384638892020144082726014804762 m

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