Question

Two guns on a battleship simultaneously fire two shells with same speed at enemy ships. If the shells follow the parabolic trajectories as shown in Fig. A.22, which ship will get hit first?

• A. $A$
• B. $B$
• C. Both at same time
• D. Need more information

Answer 1

The correct option is B $B$

Consider the time interval for the entire projectile motion is

$t_{trip}=t_{rise}+t_{fall}=2t_{rise}$

Here, $t_{rise}$ is the rise time from $0$ to the maximum height, and $t_{fall}$ is the falling time from $h$ to $0$.

In the absence of air resistance.

$t_{rise}=t_{fall}$

$h=\frac{1}{2}g{t^2}_{fall}$

Or,

$t_{trip}=2\sqrt{\frac{2h}{g}}$

So, the smaller is $h$, smaller is $t_{trip}$

Therefore, Ship $B$ will get hit first.

Hence, Option $B$ is the Correct Answer, Ship $B$ will get hit first.