Question

A cannon ball (mass = 2 kg) is fired at a target of 500 meters away. The 400 kg cannon recoils with a velocity of 2 m/s. Assuming cannon ball moves with constant velocity, when will it hit the target?

• A. 5 sec
• B. 10 sec
• C. 15 sec
• D. 2 sec

Answer 1

The correct option is A

5 sec

From the law of conservation of momentum, total momentum before firing = total momentum after firing. Therefore,
$0=massofcannon$
$\times velocityofcannon$
$+massofcannonball$
$\times velocityofcannonball$
$0=400\times (-2)+2\times v$
$\Rightarrow v=\frac{400\times 2}{2}$
$=400\text{m/s}$
Hence, the velocity of the cannonball will be 400 m/s.
Thus, time taken to hit the target=
$\frac{500}{400}=1.25s$