You have a job with an insurance company helping with the investigation of a car

Question

You have a job with an insurance company helping with the investigation of a car accident. At the scene you find a road running straight down a hill which is sloped =5° above the horizontal. At the bottom of the hill, the road goes horizontally for a very short distance to the edge of a cliff. The cliff has a height h= 400.0 ft vertical drop to the horizontal ground below. At a distance d= 30.0 ft from the base of the cliff is the wrecked car. A witness claims that the car parked somewhere on the hill, began coasting down the road on its own, taking about t1= 3.0 s before going over the edge of the cliff. The witness thinks that the driver was drunk and passed out, releasing the brake. Your boss drops a stone from the edge of the cliff and from the sound of its landing, determines that it takes t= 5.0 to hit the bottom. You are told to calculate the car's average acceleration coming down the hill using the statement of the witness and the other facts in the case. Your boss seems to suspect foul play.

Explanation / Answer

In free fall, time is independent of mass. Hence time taken by the car in dropping from cliff to the ground, t = 5s

Horizontal distance travelled by the car during dropping from cliff, x = vx* t => 30.0 ft= vx* 5s

=> Vx= 30.0ft/5s => Vx=6.00 ft/s

Car start its motion on the hill from rest so, Vo= 0 , velocity of the car at the cliff , Vx=6.00 ft/s , time spen on the hill , t1=3.0 s hence average acceleration

a = (Vx- Vo)/t1 => a = (6.00 - 0)/3.0=> a = 2.0 ft/s2

I hope this will help you.

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