Answer :
Answer:
The velocity of the launcher after the projectile is launched is -5.011 m/s
Explanation:
Here we have the mass of the cannon and cart, m₁ = 4.65 kg
Velocity of cannon and cart, v₁ = 2.00 m/s
Mass of projectile, m₂ = 50.0 g = 0.05 kg
Velocity of projectile, v₂ = 647 m/s
Velocity of the launcher, v₃ = Required
Mass of cannon and cart, launcher after launching projectile m₃ = 4.65-0.05
= 4.6 kg
Therefore, from the principle of the conservation of linear momentum, we have
Total initial momentum = Total final momentum
m₁ × v₁ = m₂ × v₂ + m₃ × v₃
Substituting gives
4.65 kg × 2.00 m/s = 0.05 kg × 647 m/s + 4.6 kg × v₃
4.65 kg × 2.00 m/s - 0.05 kg × 647 m/s = 4.6 kg × v₃
-23.05 kg·m/s = 4.6 kg × v₃
[tex]v_3 = \frac{-23.05 \, kg\cdot m/s}{4.6 \, kg} = \frac{-461}{92} m/s[/tex]
v₃ = -5.011 m/s.
Answer:
v = -4.96 m/s
Explanation:
The mass of the cart and the cannon, M₁ = 4.65 kg
The initial velocity of the cart, v₁ = 2 m/s
The mass of the projectile, M₂ = 50 g = 0.05 kg
The initial velocity of the projectile, v₂ = 647 m/s
Velocity of the launcher after the projectile is launched, v = ?
Using the principle of momentum conservation:
Momentum of the launcher before the launch = Momentum of the projectile + momentum of the launcher after the launch
M₁v₁ = M₂v₂ + M₁v
(4.65*2) = (0.05*647) + (4.65v)
9.3 = 32.35 + 4.65v
9.3 - 32.35 = 4.65v
-23.05 = 4.65v
v = -23.05/4.65
v = -4.96 m/s