A 5g bullet is fired from a 5000g gun. If the bullet leaves the gun going +800m/s, with what speed does the gun recoil?

-.8m/s

Speed of recoil of the gun = change in momentum/mass of the bullet

= 5 x 10-3 x 800/5 msec-1 = 0.8 msec-1
(Found on wiki answers (searched on google))

To find the speed at which the gun recoils, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before an event must be equal to the total momentum after the event, assuming no external forces are acting.

First, we need to determine the momentum of the bullet. The momentum (p) of an object is given by the product of its mass (m) and its velocity (v).

Given:
Mass of the bullet (m_bullet) = 5g = 0.005kg
Bullet's velocity (v_bullet) = +800m/s

Momentum of the bullet (p_bullet) = (m_bullet) x (v_bullet)

p_bullet = (0.005kg) x (+800m/s)

Next, we need to determine the momentum of the gun. Since the bullet is fired in one direction, the gun will recoil in the opposite direction.

Mass of the gun (m_gun) = 5000g = 5kg (Note: 1kg = 1000g)
Velocity of the gun (v_gun) = ? (what we're trying to find)

Using the conservation of momentum, we can write the equation:

Total initial momentum = Total final momentum

Initial momentum of the system (before firing) = Final momentum of the system (after firing)

The initial momentum of the system is the momentum of the gun before firing, which is given by:

Initial momentum of the system = (m_gun) x (0) (since the gun is at rest initially)

The final momentum of the system is the sum of the momenta of the bullet and the recoil of the gun:

Final momentum of the system = (m_bullet) x (v_bullet) + (m_gun) x (v_gun)

Since the bullet and gun have opposite directions, the final momentum becomes:

Final momentum of the system = (m_bullet) x (v_bullet) - (m_gun) x (v_gun)

Setting the initial and final momenta equal, we can solve for the velocity of the gun:

(m_gun) x (0) = (m_bullet) x (v_bullet) - (m_gun) x (v_gun)

(0) = (0.005kg) x (+800m/s) - (5kg) x (v_gun)

Simplifying the equation:

0 = 0.004kg m/s - 5kg x v_gun

Rearranging the equation:

5kg x v_gun = 0.004kg m/s

Finally, solving for v_gun:

v_gun = (0.004kg m/s) / (5kg)

v_gun = 0.0008m/s

Therefore, the gun recoils with a speed of 0.0008 m/s in the opposite direction.