Question

A policeman fires a bullet on a thief's car at rest. As the bullet is fired, the car starts accelerating by acceleration $10m/s^2$. If the speed of bullet is $720km/h$ and the initial distance of thief's car from policeman is $2km$, then after what time will the bullet hit the thief's car?

Answer 1

Let the distance travelled by car when bullet hits the car be $S$.

$\therefore$distance travelled by bullet when it hits the car is $2Km+S$.

For bullet eq is,

$\therefore$ $2\times {10}^3+S=\frac{720\times {10}^3}{3600t}$ ...($t=$time when the bullet hits the thiefs car)...(1)

For car eq is,

$S=\frac{1}{2}10t^2$ ....(2)

From eq(1) and (2) we get,

$\frac{720\times {10}^3}{3600t}-2\times {10}^3=\frac{1}{2}10t^2$

$\therefore 5t^2-2\times {10}^{3}t-200=0$

$\therefore t=400sec$

Hence bullet hit the thief's car after $400sec$.