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 24.0 degrees 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 4.00 m/s^2 for a distance of 50.0 m to the edge of the cliff, which is 30.0 m above the ocean. Find (a) the car's position relative to the base of the cliff when the car lands in the ocean and (b) the length of time the car is in the air.

Explanation / Answer

Here ,

theta = 24 degree

a = 4 m/s^2

d = 50 m

speed of the car when it leaves the incline is u

u^2 = 2 * a* d

u^2 = 2 * 4 * 50

u = 20 m/s

a) let the position of the car is at x

Now, for the trajectory

y = x * tan(theta) - 0.50 gx^2/(u * cos(theta))^2

- 50 = x * tan(- 24 degree) - 0.50 * 9.8 * x^2/(20 * cos(24 degree))^2

solving for x

x = 45.13 m

the distance from the cliff where car falls is 45.13 m

part B)

length of time in air = x/( u * cos(theta))

length of time in air = 45.13/(20 * cos(-24))

length of time in air = 2.47 s

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