Question

An armored car $2m$ long and $3m$ wide is moving at $10m{s}^{-1}$ when a bullet hits it in a direction making an angle ${\tan }^{-1}\left(\frac{3}{4}\right)$ with the length of the car as seen by a stationary observer. The bullet enters one edge of the car at the corner and passes out at the diagonally opposite corner. Neglecting any interaction between the car and the bullet, the time for the bullet to cross the car is

• A. 0.20 s
• B. 0.15 s
• C. 0.10 s
• D. 0.50 s

Answer 1

The correct option is A 0.20 s

x-component $=vcos\theta -10$ (Considering relative velocity of the bullet w.r.t. car.)
y-component $vsin\theta$
$\Rightarrow vsin\theta \cdot t=3$
$\Rightarrow (vcos\theta -10)t=2$
$\Rightarrow v\cdot \frac{3}{5}\cdot t=3\Rightarrow v=\frac{5}{t}$
$\Rightarrow (\frac{5}{t}\cdot \frac{4}{5}-10)t=2$
$\Rightarrow 4-10t=2$
$\Rightarrow 2=10t$
$\Rightarrow t=0.2seconds$