After robbing a bank, a criminal tries to escape from the police by driving at a constant speed of 55 m/s (about 125 mph). A pol
ice officer, initially at rest, starts chasing the criminal when he drives by, accelerating at a constant rate of 6.1m/s2. How long will it take the officer to catch the criminal?
We have two different types of motions, the criminal moves with uniform motion while the police do it with uniformly accelerated motion. Therefore we will use the equations of these cases. We know that by the time the police reach the criminal they will have traveled the same distance.
The distance between the police and the criminal when the first one starts the persecution is 0, its initial speed is also zero. So:
The value of the free-fall acceleration at the surface of the earth, can be obtained applying Newton's 2nd law, assuming that the only force acting on an object at the surface of the earth, is the one produced by the mass of the Earth, i.e. gravity.
This force can be expressed according the Newton's Universal Law of Gravitation , as follows:
From Newton's 2nd Law, we have:
Since the left sides in (1) and (2) are equal each other, both right sides must be equal each other also.
Simplifying the mass m, we can write the acceleration a in (2) as the acceleration due to gravity, g, as follows:
Since G is an universal constant, and the mass mE remains constant, if we double the radius of the Earth, the new value for the acceleration due to gravity (let's call it g'), is as follows:
≈ 10 m/