A man standing on very slick ice fires a rifle horizontally. The mass of the man together with the rifle is 70 kg, and the mass of the bullet is 10g.

Q:If the bullet leaves the muzzle at a speed of 500 m/s, what is the final speed of the man?

I don't know how to set this up, help?

Conservation of momentum applies. Momentum of bullet +momentum man=0

To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, provided no external forces are acting on the system.

Here's how you can set up the problem:

1. Identify the relevant quantities:
- Mass of the man and the rifle, m1 = 70 kg
- Mass of the bullet, m2 = 10 g = 0.01 kg
- Initial velocity of the bullet, v2(initial) = 0 m/s (since it starts from rest)
- Final velocity of the bullet, v2(final) = 500 m/s (given)
- Initial velocity of the man and the rifle, v1(initial) = ?
- Final velocity of the man and the rifle, v1(final) = ? (unknown)

2. Apply the principle of conservation of momentum:
According to the principle of conservation of momentum, the total initial momentum should equal the total final momentum.
Mathematically, m1.v1(initial) + m2.v2(initial) = m1.v1(final) + m2.v2(final)

3. Solve for the final velocity of the man:
Rearrange the momentum conservation equation to solve for v1(final):
m1.v1(initial) + m2.v2(initial) = m1.v1(final) + m2.v2(final)
v1(final) = (m1.v1(initial) + m2.v2(initial) - m2.v2(final)) / m1

4. Substitute the given values and solve:
v1(final) = (70 kg * v1(initial) + 0.01 kg * 0 m/s - 0.01 kg * 500 m/s) / 70 kg

Since the bullet starts from rest, its initial velocity is 0 m/s. Substituting this value into the equation, we get:
v1(final) = (70 kg * v1(initial) - 0.01 kg * 500 m/s) / 70 kg

v1(final) = v1(initial) - (0.01 kg * 500 m/s) / 70 kg

v1(final) = v1(initial) - 0.00714285714 m/s

So, the final speed of the man will be equal to his initial speed minus 0.00714285714 m/s.