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

-26 m/s (backward)

Step-by-step 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=-(mv)/(M)=-((0.52)(+75))/(1.5)=-26 m/s`

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