First slide

Projection Under uniform Acceleration

Question

A car 2 m long and 3m wide is moving at 10 m/s when a bullet hits it in a direction making an angle of $\tan^{- 1} (\frac{3}{4})$ with the car as seen from the ground. The bullet enters one edge of the car at the corner and passes out at diagonally opposite corner. Neglecting gravity, the time for the bullet to cross the car is

Moderate

A

1.0 s
B

0.4 s
C

0.2 s
D

0.6 s

Solution

Let the speed of bullet be v. The component of relative velocity in the direction of the length of the car is $v \cos θ - 10$ and in the direction of the width of the car is v $\sin θ$ . Then from s = vt.
$2 = (v \cos θ - 10) t and 3 = (v \sin θ) t$
Eliminating v, we get t = 0.2 s

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