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 25.0 m above the ocean. Find the following.
(a) The car's position relative to the base of the cliff when the car lands in the ocean.
(b) The length of time the car is in the air.

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 -25 = 0 Solve for time' t " .we get t = 2.754 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 * 2.754s = 52.46 m 2) the length of time the car is in the air = " t" = 2.754s

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