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 22.0° 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 3.52 m/s2 for a distance of 60.0 m to the edge of the cliff, which is 35.0 m above the ocean.

(a) Find the car's position relative to the base of the cliff when the car lands in the ocean.
m

(b) Find the length of time the car is in the air.
s

Explanation / Answer

The velocity of the car while rolling down the incline is
v^2 = 2aS
? v = [2aS}^2
=[2*3.52 * 60]^1/2
= 20.55 m/s
The vertical and horizontal component of velocity
vx = v cos22 = 19.05 m/s
vy = v sin22 = - 7.698 m/s(down ward)
From basic kinematic relation we have
h = ho + vy * t -0.5gt^2
0 = ho + vy * t -0.5gt^2
0.5gt^2 + 7.698 *t -35 = 0
Solve for time' t " .we get t = 2.00 s

1) the car's position relative to the base of the cliff when the car lands in the ocean
x = vx * t
= 19.05 m/s * 2.00s
= 38.1 m

2)   the length of time the car is in the air = " t" = 2.00 s

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