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 19.0° 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 3.06 m/s2 for a distance of 70.0 m to the edge of the cliff, which is 35.0 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 that

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of (theta) =19.0° below the horizontal.

The car rolls from rest(u) =0m/s down the incline with a constant acceleration of (a) =3.06 m/s2 for a distance of (s) =70.0 m to the edge of the cliff, which is 35.0 m above the ocean.

Now from the equation of motion we get

v2=u2+2as

v2 =0+2*3.06*70=428.4

v =20.697m/s

The time taken for the down the flight is

s =ut+(1/2)gt2

35m =20.697sin19*t+(1/2)gt2

6.7382t+4.905t2-35 =0

By solving the above equation we get t =2.0712s

Then the length of time for the car in the air is t =2.0712s

Then the car's relatriveposition to the base of the cliff when the car lands on the ocean is

   =20.697cos19*2.0712s =40.532m

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