Question

A 900kg cannon fire 100kg shells with muzzle velocity of 75m/s. Calculate the recoil velocity of the cannon relative to the ground​

Answer 1

Given :

• Mass of the Cannon = 900 kg
• Mass of the shell = 100 kg
• Velocity of cannon = 75 m/s

To find :

The recoil Velocity of the Cannon.

Solution :

Let the mass of cannon $\bf{m_{1}}$.

Let the mass of shell $\bf{m_{2}}$.

Let the Recoil velocity of cannon $\bf{v_{1}}$.

Let the velocity of shell $\bf{v_{2}}$.

From the law of conservation of momentum , we get :

$\boxed{\bf{P = P'}}$

Where :

• P = Momentum

But we know that ,

$\underline{\bf{(P) = mv}}$

Where :

• P = Momentum
• m = Mass
• v = Velocity

Substituting it in the conservation of momentum , we get :

$:\implies \bf{P = P'}$

Since, the total momentum is 0 here, we get :

$:\implies \bf{m_{1}v_{1} + m_{2}v_{2} = 0}$

Where :

• m = Mass of the body
• v = Velocity

Now using the above equation and substituting the values in it, we get :

$:\implies \bf{m_{1}v_{1} + m_{2}v_{2} = 0}$

$:\implies \bf{900 \times v_{1} + 100 \times 75 = 0}$

$:\implies \bf{900 \times v_{1} = - 7500}$

$:\implies \bf{v_{1} = -\dfrac{7500}{900}}$

$:\implies \bf{v_{1} = - 8.4 (approx.)}$

$\boxed{\therefore \bf{v_{1} = - 8.4\:ms^{-1}}}$

Hence, the recoil Velocity is - 8.4 m/s