Question

A gun is fired at a target. At the moment of firing, the target is released and allowed to fall freely under gravity. Then the bullet:
(Assume initial aim to be precise)
A) misses the target by passing above it
B) hits the target
C)misses the target by passing below it
D) may or may not hit the target

Answer 1

Hint: The objects falling towards the earth under the gravitational force alone, are called freely falling objects and such fall is called free fall, whenever an object falls towards the earth, an acceleration is involved, this acceleration is due to the earth's gravitational pull and is called acceleration due to gravity

Complete solution:
As when the bullet is fired the bullet and target both are at rest. So, they both will have initial velocity
\[i.e.{\text{ }}u{\text{ }} = {\text{ }}0.\]
Now, we will have to find distance of both gun and target
Applying equation of motion for distance
$S = ut + \dfrac{1}{2}\mathop {gt}\nolimits^2 $
where s is distance, u is initial velocity = 0
g is acceleration due to gravity and it is time.
Substituting the values in equation
As u = 0
$\Rightarrow S = \dfrac{1}{2}\mathop {gt}\nolimits^2 $ (for both bullet and target)
So, as both of them cover equal distance they will touch each other. The bullet will cover a projectile path , where
\[\Rightarrow R = \dfrac{{{u^2}\sin 2\theta }}{g}\]
The bullet will be fired at an angle , with a vertical velocity so that the range of the bullet , correctly meets with the distance travelled due to free fall. The initial vertical velocity at which the gun is fired is near to zero, which means that R=S, thus hitting the target.
Now we will match the options with our observations:
a) Misses the target by passing above it: As both covers equal distance so they will touch each other and do not miss the target. Thus, this option is not correct.
b) Hits the target: This will exactly happen as moving down they cover equal distance so an instant gun will hit the target. Thus, this option is correct.
c) Miss the target by passing below it: As both covers equal distance so they will touch each other and do not miss the target. Thus, this option is not correct.
d) May or may not hit target: It will definitely hit target as they both are covering equal distance. So, there is no probability that it will not hit the target. Thus, this option is not correct.

Our required answer is option (B), that is Hits the target.

Note: If both the bodies were released at the same time in vacuum it means that there is no air resistance as in case of free fall of objects, then both the objects would reach earth surface within the same duration of time. When this condition occurs both the objects hit with each other in such cases.