Question

In the climax of a movie, the hero jumps from a helicopter and the villain chasing the hero also jumps at the same time from the same level. After sometime when they were at the same horizontal level, the villain fires bullets horizontally towards the hero. Both were falling with constant acceleration\[2\,m/{s^2}\], because of the parachute. Assuming the hero to be within the range of the bullet, and the air resistance force on the bullet is negligible. Which of the following is correct?
A. Bullet will hit the hero
B. Bullet will pass above the hero
C. Bullet will pass below the hero
D. Bullet will definitely hit the hero, if both were falling with constant acceleration \[4m/{s^2}\] instead of \[2\,m/{s^2}\]

Answer 1

Hint: Consider the net acceleration of both hero and bullet to answer this question. We know that acceleration due to gravity does not affect the horizontal motion of the projectile. Use this concept to answer this question.

Complete step by step answer:
We will consider the net acceleration of both hero and bullet to answer this question. We have given that the acceleration of the hero is reduced because he descends with a parachute. The air resistance opposes the gravitational force acting on the hero that reduces the acceleration of the hero. In the case of the bullet, the area of the bullet is very small. Therefore, the air resistance will not act on the bullet to reduce the net acceleration of the bullet.
We see for the first second, the hero covers 2 m distance in the downward direction and for the next second he will cover 4 m distance and so on. We know that the acceleration due to gravity does not affect the horizontal motion of the bullet. Therefore, the bullet will not move in the downward direction for a certain interval of time. In the meantime, the hero will cover some downward distance and therefore, the bullet will pass above him.

To hit the bullet to the hero, the villain should have fired the bullet at some distance below the position of the hero at that instant of time. Therefore, the option (A) is incorrect.
The bullet will pass below the hero if the hero is not moving in the downward direction because by the time bullet reaches the hero it has moved slightly in the downward direction,
Therefore, the option (C) is incorrect.
Bullet will not hit the hero, even if both were falling with constant acceleration \[4m/{s^2}\] instead of \[2\,m/{s^2}\]. Therefore, the option (D) is incorrect.

So, the correct answer is “Option B”.

Note:
Students should note that the acceleration due to gravity does not affect the horizontal motion of the projectile. From Archimedes principle, we know that objects with less volume sink in the water quickly compared to objects with large volume. The same applies with the objects descending in the air.