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 23.0° 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 3.67 m/s2 for a distance of 35.0 m to the edge of the cliff, which is 25.0 m above the ocean.

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

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

Explanation / Answer

here,

s = 35 m

constant accelration , a = 3.67 m/s^2

the speed of car at the edge of cliff , u = sqrt(2*a*s)

u = sqrt(2*3.67* 35) = 16.1 m/s

theta = 23 degree

a)

let the time taken by car in air be t

h = 25 m = u * sin(theta) * t + 0.5 * g * t^2

25 = 16.1 * sin(23) * t + 0.5 * 9.81 * t^2

solving for t

t= 1.71 s

the car's position relative to the base of the cliff when the car lands in the ocean , x= u * cos(theta) * t

x = 16.1 * cos(23) * 1.71 m = 25.4 m

b)

the time taken by car in air is 1.71 s

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