Question

A cannon of mass 1400 kg fires a cannon ball of mass 70 kg at a speed of 60 m/s. Calculate the velocity of the cannon, both magnitude and direction.

Answer 1

Given:

Mass of Cannon = 1400 kg

Mass of ball = 70 kg

Speed of ball = 60 m/s

Let's find the velocity of the cannon.

To find the velocity of the cannon, apply the conservation of momentum:

`m_1u_1+m_2u_2=m_1v_1+m_2v_2`

SInce they were both at rest befoe firing, we have:

u1 = u2 = 0 m/s

Where:

m1 = 1400 kg

m2 = 70 kg

v2 = 60 m/s

v1 is the speed of the cannon, let's solve for v1.

We have:

`\begin{gathered} 1400(0)+70(0)=1400* v_1+70*60_{}_{} \\ \\ 0=1400v_1+4200 \\ \\ \text{Subtract 4200 from both sides:} \\ -4200=1400v_1+4200-4200 \\ \\ -4200=1400v_1 \\ \\ (-4200)/(1400)=(1400v_1)/(1400) \\ \\ -3=v_1 \\ \\ v_1=-3\text{ m/s} \end{gathered}`

Therefore, the velocity of the cannon is -3 m/s.

Since the velocity of the cannon is negative, it means that the velocity of the cannon is in the opposite direction to the motion of the ball.

Therefore, the velocity of the cannon is -3 m/s ,which implies that the velocity of the cannon is in the opposite direction to the motion of the ball.

ANSWER:

-3 m/s, in the opposite direction to the motion of the ball.