what is the mass of a cannonball whose velocity is 100 m/s if it were shot from a 2500 kg cannon that recoiled at a speed of 3 m/s

We can solve this problem by using the law of conservation of momentum: in fact, the total momentum of the ball-cannon system before and after the shot must be equal.

Before the shot, the total momentum is zero, since both objects are at rest:

[tex]p=0[/tex] (1)

After the shot, the total momentum is: given by:

[tex]p=mv+MV[/tex] (2)

where :

m kg is the mass of the cannonball

v = 100 m/s is the velocity of the ball

M = 2500 kg is the mass of the cannon

V = -3 m/s is the recoil velocity of the rifle (in the opposite direction to the ball

Since the toal momentum is conserved, (1) = (2), therefore we can solve for m, the mass of the cannonball:

[tex]0=mv+MV\\m=-\frac{MV}{v}=-\frac{(2500)(-3)}{100}=75 kg[/tex]

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