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 24.0° 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 3.82 m/s2 for a distance of 65.0 m to the edge of the cliff, which is 20.0 m above the ocean. (a) Find the car's position relative to the base of the cliff when the car lands in the ocean. (b) Find the length of time the car is in the air.

Explanation / Answer

Initial Velocity, u = 0
Acceleration, a = 3.82 m/s^2
Distance, s = 65.0 m

Final Velocity, Vf = ?

Vf^2 = u^2 + 2*a*s
Vf^2 = 0 + 2* 3.82*65.0
Vf = 22.3 m/s

Now, Horizontal Velcoity,
Vx = 22.3 * cos(24)
Vx = 20.37 m/s

Vertical Velocity,
Vy = 22.3 * sin(24)
Vy = 9.1 m/s

Time taken by car to reach ocean, t
S = u*t + 1/2at^2
20 = 9.1*t + 1/2*9.8*t^2
t = 1.3 s

Horizontal distance travelled in this time,
Sx = Vx*t
Sx = 20.37 * 1.3 m
Sx = 26.5 m

(A) Position relative to the base of the cliff when the car lands in the ocean, Sx = 26.5 m
(B) Length of time car is in air, t = 1.3 s

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