Question

A gun is aimed at a target in a line of its barrel. The target is released and allowed to fall under gravity at the same instant the gun is fired. The bullet will
A. Pass above the target
B. Pass below the target
C. Hit the target
D. Certainly miss the target

Answer 1

In the given question, if observed carefully, only the vertical motion of the bullet is to be taken into consideration and also of the target as they are not having any horizontal component of the motion and only that would help us determine the outcome.

Complete answer:
It is given that the gun is aimed at a target in a line of its barrel and at the same instant as it is fired, the target is also released.
Here the target undergoes only the vertical motion while the bullet has to undergo both horizontal and vertical motion (i.e. it undergoes a projectile motion).
However only the vertical component of the bullet's motion determines if it actually hits the target or not.
Let ‘t’ be the time at which the bullet interacts with the target.
Since,
1. Initially both bullet and the target were at rest, their initial velocity will be zero. $(u=0)$
2. The bullet and the target were released at the same instant.
3. The bullet and the target experience the same downward acceleration due to gravity.$(a=g)$
From the relation: $S=ut+\dfrac{1}{2}g{{t}^{2}}$
It can be observed that for time ‘t’ both the bullet and the target cover the same vertical displacement, hence assuring that the bullet will hit the target at time ‘t’.

Therefore, the correct option would be option (C) Hit the target.

Note:
The acceleration due to gravity is independent of shape, size or mass of an object.
However, it varies in small amounts as the distance of the object from the Earth’s surface is varied.
Taking the bullet’s horizontal component of motion into consideration while solving the above question can lead to incorrect results.