A man is in a boat out away from shore. The mass of the man and the boat is 188 kg. The boat is not moving. The man throws and anchor with a mass of 22 kg straight out from the boat with a speed of 13.8 m/s. What is the resulting speed of the boat?

22*13.8 - 188 v = 0

v = 1.61 m/s

To find the resulting speed of the boat, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the man throws the anchor is equal to the total momentum after he throws it.

The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v). So, the initial momentum of the man and the boat before the anchor is thrown can be expressed as:

Initial momentum = (mass of man + mass of boat) × 0 (since the boat is not moving)

Initial momentum = 188 kg × 0 = 0 kg·m/s

After the anchor is thrown, the man and the boat will gain momentum in the opposite direction. The momentum of the man and the boat after the anchor is thrown can be calculated by adding their individual momenta.

Final momentum = (mass of man + mass of boat + mass of anchor) × velocity of boat

Final momentum = (188 kg + 22 kg) × final velocity of the boat

Now, we'll equate the initial and final momenta to find the final velocity of the boat.

0 kg·m/s = (188 kg + 22 kg) × final velocity of the boat

0 kg·m/s = 210 kg × final velocity of the boat

To solve for the final velocity of the boat, we divide both sides of the equation by the total mass:

final velocity of the boat = 0 kg·m/s / 210 kg

final velocity of the boat = 0 m/s

Therefore, the resulting speed of the boat is 0 m/s.