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 16° 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 4.1 m/s^2 and travels 47 m to the edge of the cliff. The cliff is 40 m above the ocean.
a. How long is the car in the air? The acceleration of gravity is 9.81 m/s^2. Answer in units of s.
2. 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.

Explanation / Answer

a) By v^2 = u^2 + 2as =>v^2 = 0 + 2 x 2.59 x 45 =>v = v233.1 =>v = 15.27 =>Vy = vsin16* = 15.27 x 0.28 = 4.21 m/s & Vx = vcos16* = 15.27 x 0.96 = 14.68 m/s Thus by s = ut + 1/2gt^2 =>50 = 4.21 x t + 1/2 x 9.8 x t^2 =>4.9t^2 + 4.21t - 50 = 0 =>t = [-4.21+/-v{(4.21)^2 - 4 x 4.9 x (-50)}]/[2 x 4.9] =>t = [-4.21+/-31.59]/[9.8] =>t = 2.79 sec Thus by R = [Vx] x t =>R = 14.68 x 2.79 = 41m (b) t = 2.79 sec

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