Question

A 1.5kg cannon is loaded with a 0.52 kg ball . The cannon is ignited and launches the ball forward with speed of 75m/s. Determine the post explosion velocity of the cannon.

Answer 1

Answer:

-26 m/s (backward)

Explanation:

We can solve this problem by using the law of conservation of momentum.

In fact, the total momentum momentum of the cannon + ball system must be conserved before and after the explosion.

Before the explosion, they are both at rest, so the total momentum is zero:

p = 0

After the explosion, the total momentum is:

$p=MV+mv$

where

M = 1.5 kg is the mass of the cannon

m = 0.52 kg is the mass of the ball

v = +75 m/s is the velocity of the ball

V is the velocity of the cannon

Since the momentum is conserved, we can equate the two expressions:

$0=MV+mv$

And solving, we find V:

$V=-\frac{mv}{M}=-\frac{(0.52)(+75)}{1.5}=-26 m/s$

where the negative sign means the direction is opposite to that of the ball.