A bullet fired straight up from the surface of the moon would reach a height of s = 832*t - 2.6*t^2 m after t sec. On earth, in the absence of air, its height would be s = 832*t - 16*t^2 m after t second. How long will bullet be aloft in each case?
The distance traveled by a bullet fired at 832 m/s after t seconds on the Moon is given by: s = 832*t - 2.6*t^2 m
The bullet stops when the speed is zero. When speed is 0, ds/dt = 0
=> 832 - 5.2t = 0
=> t = 832/5.2
=> t = 160
The time the bullet is aloft on the Moon is 160 s
For Earth, the distance traveled by a bullet fired at 832 m/s after t s is given by s = 832*t - 16*t^2 m
It stops when ds/dt = 0
=> 832 - 32t = 0
=> t = 26 s
The bullet is aloft for 160 s on the Moon and for 26 seconds on the Earth.