Respuesta :
(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
(a) The backward or recoil velocity of the gun is calculated by applying the principle of conservation of linear momentum.
- let the backward or recoil velocity of the gun = u₂
m₁u₁ + m₂u₂ = 0
m₂u₂ = -m₁u₁
[tex]u_2 = -\frac{m_1u_1}{m_2} \\\\u_2 = - \frac{0.1 \times 400}{5} \\\\u_2 = -8 \ m/s[/tex]
Thus, the recoil or backward velocity of the gun is 8 m/s.
(b) determine if the bullet can 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
[tex]a = \frac{v^2 -u_1^2}{2s} \\\\a = \frac{(266.67)^2 -(400)^2}{2\times 0.04} = -1.111 \times 10^6 \ m/s^2[/tex]
Finally, determine the distance traveled by the bullet when it comes to a complete stop, that is the final velocity = 0
[tex]v_f^2 = v^2 + 2ad\\\\2ad = v_f^2 - v^2\\\\d = \frac{v_f^2 - v^2}{2a} \\\\d = \frac{(0) - (266.67)^2}{2(-1.111\times 10^6)} \\\\d = 0.032 \ m[/tex]
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 penetrate the plank completely.
To learn more about linear momentum visit: https://brainly.com/question/15869303