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 20.0° 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 3.21 m/s2 for a distance of 70.0 m to the edge of the cliff, which is 30.0 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

given

angle = 20 degrees below the x axis

acceleration a = 3.21 m/s^2

height = 30 m

from the relation

vf^2-vi^2 = 2as

here vi = 0

vf^2 = 2*3.21*70

vf = 21.19 m/s

now

from the equation

y = vi*t+1/2ay*t^2

-30 = 21.19*sin(-20)*t-1/2*9.8*t^2

-7.25t-4.9t^2+30 = 0

4.9t^2+7.25t-30 = 0

it is a qudratic equation

roots are

b) t = 1.84 sec

a) x = vi*cos(-20)*t

x = 21.19*cos(-20)*1.84

x = 36.64 m

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