a bullet of mass 20g is horizontally fired with a velocity of mass 150m/sec from a pistol of mass 20g.what is the recoil velocity of the pistol?
I doubt if the bullet has the same mass as the pistol. Something is wrong.
Mb*Vb=Mp*Vp
To find the recoil velocity of the pistol, we can use the principle of conservation of momentum. According to this principle, the total momentum before the firing is equal to the total momentum after the firing.
The momentum of an object is given by the product of its mass and velocity:
Momentum (p) = Mass (m) × Velocity (v)
Let's assign variables to the given values:
mass of bullet (m₁) = 20 g = 0.02 kg
velocity of bullet (v₁) = 150 m/s
mass of pistol (m₂) = 20 g = 0.02 kg
recoil velocity of pistol (v₂) = ?
Using the conservation of momentum equation:
(m₁ × v₁) + (m₂ × v₂) = 0
Substituting the values:
(0.02 kg × 150 m/s) + (0.02 kg × v₂) = 0
3 kg·m/s + 0.02 kg·m/s = 0.02 kg·m/s (since 150 m/s × 0.02 kg = 3 kg·m/s)
0.02 kg·m/s + 0.02 kg·m/s = 0.02 kg·m/s
0.04 kg·m/s = 0.02 kg·m/s
Therefore, the recoil velocity of the pistol is 0.02 m/s.
To find the recoil velocity of the pistol, we can use the principle of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity. According to the conservation of momentum, the total momentum before an event is equal to the total momentum after the event, as long as no external forces are acting on the system.
Let's assume the bullet moves in the positive direction and the recoil velocity of the pistol is in the negative direction.
Given:
Mass of bullet (m1): 20 g = 0.02 kg (convert grams to kilograms)
Velocity of bullet (v1): 150 m/s
Mass of pistol (m2): 20 g = 0.02 kg
Recoil velocity of pistol (v2): ?
Using the conservation of momentum formula:
Initial momentum = Final momentum
(m1 * v1) + (m2 * 0) = (m1 * 0) + (m2 * v2)
Since the bullet is fired horizontally, its initial vertical velocity is zero. Also, since the mass of the pistol is much larger than the bullet, we can assume that the initial velocity of the pistol (before firing) is negligible.
Therefore, the equation simplifies to:
m1 * v1 = m2 * v2
Substituting the values:
(0.02 kg) * (150 m/s) = (0.02 kg) * v2
Simplifying:
3 kg m/s = 0.02 kg * v2
Dividing both sides by 0.02 kg:
150 m/s = v2
Thus, the recoil velocity of the pistol is 150 m/s in the opposite direction of the bullet's velocity.