(a) the recoil or backward velocity of the gun is 8 m/s.
(b) the bullet cannot completely penetrate the plank.
<u>The given parameters include;</u>
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
<u>To calculate the following:</u>
(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 bullet traveled 4 cm and lost ¹/₃ of u₁
- the remaining distance to completely penetrate the plank = 6 cm
- the final velocity of the bullet at 4 cm, v = 400 - ¹/₃ x 400 m/s = 266.67 m/s
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.
<u>To learn more about linear momentum visit: </u>brainly.com/question/15869303