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# A 3000 kg cannon recoils with a velocity of 1 m s−1, when a 15 kg cannon ball is fired from it. If the ball is aimed a target 400 m away, calculate the force (in N) that the ball exerts on the target, when it hits it.750

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Solution

## The correct option is A 750Given The mass of the cannon ball, m1=15 kg The mass of the cannon, m2=3000 kg Distance to the target, d=400 m The recoil velocity of the cannon, v2=1 m s−1 If the velocity of the cannon ball is v1, then according to the law of conservation of momentum, m1v1+m2v2=0, as both the cannon and the cannon ball are initially at rest. v1=−m2v2m1=300015=200 m s−1 According to the third equation of motion, v2−u2=2as v=200 m s−1; u=0; s=d=400 m The acceleration of the cannon ball, a=v22s=200×2002×400=50 m s−2 The force exerted by the cannon ball on the target is given by Newton's second law of motion as: F = m1a ⟹F=15 kg×50 m s−2 ⟹F=750 N

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