JEE Main & Advanced Physics Two Dimensional Motion JEE PYQ - Two Dimensional Relative Motion

The initial speed of a bullet fired from a rifle is 630 m/s. The rifle is fired at the centre of a target 700 m away at the same level as the target. How far above the centre of the target? [JEE ONLINE 11-04-2014]

A) 1.0m

B) 4.2 m

C) 6.1 m

D) 9.8 m

Correct Answer: C

Solution :

[c] Let t be the time taken by the bullet to hit the target.

\[\therefore \]\[700m=630m{{s}^{-1}}t\]\[\Rightarrow \]\[t=\frac{700m}{630m{{s}^{-1}}}=\frac{10}{9}\sec \]

For vertical motion,

Here, u = 0

\[\therefore \]\[h=\frac{1}{2}g{{t}^{2}}\] \[=\frac{1}{2}\times 10\times {{\left( \frac{10}{9} \right)}^{2}}\]

\[=\frac{500}{81}m=6.1m\]

Therefore, the rifle must be aimed 6.1 m above the centre of the target to hit the target.