Problema Solution
A rocket is shot straight up in the air from the ground at a rate of 51 feet per second. The rocket is tracked by a rangefinder that is 494 feet from the launch pad. Let d represent the distance from the rocket to the rangefinder and t represent the time, in seconds, since "blastoff". Express d as a function of t.
Answer provided by our tutors
Actually, the speed at which the bullet will fall back to the ground wont really depend on how fast it left the gun. This is because the force of air resistance depends on velocity. As the bullet falls, it speeds up (due to gravity). The faster it goes, the more air resistance it feels. Eventually it reaches a speed at which the force of gravity pushing down on it is equal to the force of air resistance pushing up. When all the forces balance out like this, the bullet stops speeding up - this is called the terminal velocity.
In order to calculate the exact terminal velocity of your bullet, there are a lot of things that you would have to know - such as the weight and shape of the bullet, the wind speed, the altitude, etc. One estimate that I found online is about 300 ft/sec (about 200 mph), which sounds like a reasonable guess.