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 16.0° 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 2.59 m/s2 for a distance of 45.0 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.
m

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

Explanation / Answer

Data: Angle, = 16 deg below horizontal Acceleration of the car, a = 2.59 m/s^2 Distance traveled along the cliff, x = 45 m Height of the edge of the cliff from ocean, h = 20 m Initial velocity of the car, vo = 0 m/s Let Velocity of car on reaching edge of the cliff = v Solution: From the equations of motion, v^2 = vo^2 + 2 a x        = 0 + (2 * 2.59 * 45 )        = 233.1 v = 15.27 m/s Motion in air: ( parabolic path ) Vertical displacement, y = vy t + (1/2) a t^2                                  - h = ( v sin * t ) + 0.5 * (-g) t^2                                  - 20 = -15.27 sin16 t - 0.5 * 9.8 t^2                                  4.9 t^2 + 4.21 t - 20 = 0 By solving the quadratic equation, t = 1.63 s (a) Position of the car relative to the base of the cliff: x = v cos * t    = 15.27 cos 16 * 1.63    = 23.93 m (b) Length of the time, t = 1.63 s

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