A 50 kg cannonball hits a war tank vehicle of 12,000 kg that is initially at rest. The cannonball embeds in the tank and both move at the same velocity for 50 cm until they both come to a rest. The coefficient of friction between the tank and the pavement is 0.450. What was the initial velocity of the cannonball

506.1 m/s

Explanation:

Let the initial velocity of cannonball be 'u' and final common velocity after collision be 'u₁'.

Given:

Mass of the cannonball (m) = 50 kg

Mass of the war tank (M) = 12,000 kg

Initial velocity of the tank (U) = 0 m/s

Distance moved by the system after collision (d) = 50 cm = 0.50 m

Coefficient of friction (μ) = 0.450

At the time of collision, momentum is conserved. So,

Initial momentum = Final momentum

Now, as the system moves along the rough surface, the system eventually stops after traveling a certain distance.

The acceleration due to friction is given as:

The negative sign implies that acceleration is acting to reduce the velocity.

Now applying the following equation of motion, we have:

Now, solving for 'u', we get:

Therefore, the initial velocity of the cannonball was 506.1 m/s.

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