A car is parked on a cliff overlooking the ocean on an incli

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 30.0 m to the edge of the cliff, which is 40.0 m above the ocean.

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

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

Solution

v = sqrt [2 a d] = sqrt [2 * 3.52 * 30] = 14.53 m/s

v₀ = v sin theta = 14.53 * sin 22 = 5.45 m/s

v² = v₀² + 2 a d

v_y = sqrt [v₀² + 2 a y] = sqrt [5.45² + 2 * 9.8 * 40]

= 28.52 m/s

t = v_y - v_o / a = 28.52 - 5.45 / 9.8

t = 2.35 s

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a) v_x = v cos theta = 14.53 * cos 22 = 13.47 m/s

x = v_x t = 13.47 * 2.35

= 31.65 m