A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 19◦ 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 4.2 m/s2 and travels 40 m to the edge of the cliff. The cliff is 28 m above the ocean.
1. How long is the car in the air?
2. What is the car’s position relative to the base of the cliff when the car lands in the ocean?

Question

A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 19◦ 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 4.2 m/s2 and travels 40 m to the edge of the cliff. The cliff is 28 m above the ocean.
1. How long is the car in the air?
2. What is the car’s position relative to the base of the cliff when the car lands in the ocean?

osprey · Answer

I've just had a go at this one, and enclose an enclosure as you might say. Bit of a silly person, the former driver of the now sopping wet and ruined car. Maybe the driver was in a hurry - most people seem to be these days. I don't really see why the questioners have to give what seem to be awkward numbers, and awkward algebra on top of the actual idea behind the solution to the problem. Maybe I'm missing something, I don't know. That's just me, I guess. http://perendis.webs.com

osprey · Answer

A further thought. In the problem, the car is rolling under gravity down a straight road - bit like a very long plank towards the cliff edge. That's the shortest distance between the two points - the car's starting point and the cliff edge. However, in physics, there's another shortest "distance", if you call TIME a "distance". Finding the profile (no longer like that of a plank) of a road which makes the car - accelerated by gravity - go between the starting point and the cliff edge in the SHORTEST POSSIBLE TIME is a very popular problem in physics. The profile is very much more curved, so that it's no longer the shortest physical distance between the point, but it is the shortest time. It has a special name, which may or may not be brachistochrone, I can only vaguely remember.
I've often been curious about the shape of the ski jump ramp used in winter sports before the skier launches themselves downhill.
The maths which covers this sort of thing is given the title of "the calculus of variations". A US physicist called RICHARD P FEYNMAN was very interested in it. But then he had a Nobel prize in physics, and wrote some books called "lectures in physics".