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 17.0° 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 2.75 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.
m

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

Explanation / Answer

to find the velocity of the car on reaching the edge of the cliff

from equation of motion

v^2 - vo^2 = 2*a*s

v^2 -0^2 = 2*2.75*35

v = 13.8 m/s

at the edge of the cliff

along horizantal

vx = v*cos17

ax = 0

x = vx*T

T = x/Vx ...........(1)

along vertical

vy = -v*sin17 = 13.8*cos17 = 13.2 m/s

ay = -g = -9.8 m/s^2

y = -h = -25 m

from equations of motion

y = vy*T + 0.5*ay*T^2...........(2)

1 & 2

y = -tan17*x - 0.5*g*x^2/vx^2

for y = -25

-25 = -tan17*x-4.9x^2/13.2^2

x = 24.8 m <<------------------answer

part(b)

time T = x/vx = 24.8/13.2 = 1.88 s <<------------------answer

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