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 40.0 m above the ocean.

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

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

Answer 1

a)

Herer as shown in the figure,the angle made by the surface of hill with below the horizontal or the angle of the incline with the horizontal is given by,

Also let the position of the car is initially at the point A.

When the car leaves in neutral,the car moves travels a distance of 70m down the incline and reaches the edge of the cliff at point B as shown.

Also given the hieght of point B from the sea level is given by 40m.

ie,We have

The hieght of point B from ocean,

Here the ocean will starts from point O.

Angle of inclination,

So,From the

So,

We have the edge of the cliff is at point B,

So,the base of the cliff is at point C.

When the car reaches at the ocean at point O,the relative distance between the base of the cliff and the the position of car at this moment,is,CO

ie, relative distance between the base of the cliff and the the position of car when reaches ocean,

b)

We have from ,

We have

So,

So,

Now consider the motion of the car down the incline from the initial point(point A) to the the point O when it reaches the ocean ,

Here we have the acceleration of the car,

Distance travels from A to O,

Initial velocity at point A,

So,The time taken for he motion,from A to O,

We have the Newtons 2nd equation of motion,

ie,

So,

So,Total time for the car in air,