Robin fired a bullet of mass 100 gm from a gun of mass 5 kg. The bullet leaves the gun with a speed of 400 m/s. After penetrating 4 cm of a plank of 10 cm, the bullet loses one third of its initial velocity. a. Calculate the backward velocity of the gun?
b. Can the bullet penetrate the plank of the wood completely? Explain mathematically.

please help

(a) The recoil or backward velocity of the gun is 8 m/s.

(b) The bullet cannot penetrate the plank of the wood completely.

The given parameters include;

mass of the bullet, m₁ = 100 g = 0.1 kg

mass of the gun, m₂ = 5 kg

initial velocity of the bullet, u₁ = 400 m/s

thickness of the plank, x = 10 cm

To calculate the following:

(a) the backward velocity of the gun

let the backward velocity of the gun = u₂

Apply the principle of conservation of linear momentum.

m₁u₁  + m₂u₂ = 0

m₂u₂ = -m₁u₁

Thus, the recoil or backward velocity of the gun is 8 m/s.

(b) Can the bullet penetrate the plank of the wood completely ?

the acceleration of the bullet is calculated as;

v² = u₁² + 2as

2as = v² - u²

Finally, determine the distance traveled by the bullet when it comes to a complete stop, that is the final velocity = 0

d = 3.2 cm

The total distance traveled by the bullet inside the plank = 4 cm + 3.2 cm = 7.2 cm

Therefore, the bullet cannot completely penetrate the plank.

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