Physics Projectile Motion

Question

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 17 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 4.8 m/s 2 and travels 43 m to the edge of the cliff. The cliff is 30 m above the ocean. (a)How long is the car in the air? The acceleration of gravity is 9.81 m/s 2 . Answer in units of s.

(b) What is the car’s position relative to the base of the cliff when the car lands in the ocean? Answer in units of m.

Answer 1

Bio

At the bottom of the incline v²= u² + 2as,,, u=0. a = 4.8, s = 43, so v = 20.3 m/s

So the horizontal velocity at that point will be 20.3 cos 17 = 19.4 m/s, and the vertical velocity downward 20.3 sin 17 = 5.94 m/s

To find the time in this air, this is the time it takes the car to fall 30 m.

s = ut + 0.5 a t²

30 = 5.94 t + 0.5 x 9.81 t²

4.905 t² - 5.94t - 30 = 0

giving t = 3.2 s from graphing it and using trace

So horizontal distance travelled = 3.2 x 19.4 = 62.08 m

Mike