Question

A gunman-in-training is practicing his shooting at the range. He holds his gun at the same height as his target that is 50 m away. He shoots the bullet with a horizontal velocity of 100m/s and an initial upwards velocity of 2 m/s. a) How much time would it take for the bullet hit the target? b) How far above or below the target does the bullet hit? (Don't forget to mention above or below) c) What upward velocity should he shoot at if he wants to his directly at the target, assuming he shoots the bullet with the same horizontal speed? d) For the last exercise of his training, the gunman-in-training has to shoot a falling target. The target is dropped from rest 50 m horizontally, at a height of 25 m above his gun. If he shoots strictly horizontally, how long after the target is dropped should he pull the trigger? Use the following to help you answer this question. (i) You should already know how long it takes for the bullet to reach target’s horizontal position from a previous part of the problem.

Determine how far the bullet would fall during this time. (ii) Then you want to determine the total vertical displacement the target has to travel to be at the same place as the bullet. (iii) Now determine how long it would take for the target to travel that total vertical displacement. (iv) Finally, determine how long after the target is dropped should the gunman-in-training pull the trigger. (e) *BONUS* The gunman-in-training is simply too impatient to wait that long. Instead, he wants to pull the trigger once the target gets dropped. At what upwards velocity should he shoot with, while keeping the same horizontal velocity, in order to hit the target as it is falling? (You’re on your own for this one, but you can follow the same type of logic.)

Answer 1

Part A) The time taken by the bullet to reach the target

Part B) Now the vertical position of the bullet after this time

Here negative sign indicates below the target.

Part C) In order to hit the target, his upward velocity should be such that, the time of flight is equal to the time taken to travel the horizontal distance.

Part D) Time taken by the target to reach the same horizontal level is given by

Time after which he must shot the target

So the trigger must be pulled after 1.76 s of dropping the target.

Part E) This time the time of flight of the target and the bullet must be the same i.e