Physics (momentum)?

Question

Note: Take East as the positive direction.
A 85kg fisherman jumps from a dock into a 130kg rowboat at rest on the West side of the dock.
If the velocity of the fisherman is 5.5m/s to the West as he leaves the dock, what is the final velocity of the fisherman and the boat? Answer in units of m/s.

Please help me with this, i cant figure it out, thanks in advance.

Answer 1

This problem involves the law of conservation of momentum.

Sum of initial momentum = Sum of final momentum

Mass of fisherman, mf= 85 kg
Mass of boat, mb = 130 kg
Initial velocity of fisherman vf = -5.5 m/s (negative because going west, with east being positive)
Initial velocity of boat vb = 0 m/s
Final velocity of fisherman and boat, vfb

mf * vf1 + mb * vb = (mf + mb) * vfb

vfb = (mf * vf1 + mb * vb) / (mf + mb)
= (85 kg * -5.5 m/s + 130 kg * 0 m/s) / (85 kg + 130 kg)
= -2.17 m/s

So the final velocity of the boat and fisherman is -2.17 m/s, indicating that both are traveling west since going east is positive.

Answer 2

According to Law of Conservation of momentum, the total initial momentum of both fisherman and the boat is equal to the total final momentum of fisherman and the boat.
Let the initial momentum of the fisherman be mf x uf
Let the initial momentum of the boat be mb x ub
Total intial momentum = mf x uf + mb x ub
........................."............= 85 x 5.5 + 130 x 0
.........................."...........= 467.5 Kg.m
As the fisherman is in the boat, the final momentum is a combined one. Combined mass = 215 Kg
Let the velociy of the combined mass(fb) be v(fb)
Therefore, the final combined momentum = 215 x v(fb) Kg.m
By law of coservation of momentum, 467.5 = 215 V(fb)
v(fb) = 467.5 / 215 = 2.174 m/s
As the fisherman jumps towards west, the velocity too will be towards west. It is given that EAST is the +ve side. As the boat with the fisherman moves towards west this velocity is expressed as - 2.174 m/s
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Answer 3

the respond is in the hint itself P preliminary = P very final The preliminary momentum of pupil and jacket is 0 as they are the two no longer moving the excellent momentum is the momentum of boy and jacket after he throws the jacket 0 = m1x v1 + m2 x v2 = 3 x 14 + 80 two x v2 v2 = - 3 x 14 / 80 two = - 0.5 m/s The destructive sign shows that he strikes in a direction opposite to jacket , so as that the sum of his momentum and jacket's momentum is 0 As there is not any friction he will proceed to pass with out loss of velocity

Answer 4

Use the principle of conservation of momentum.

The total initial momentum of man+boat is:

(m_man)(v_man) + (m_boat)(0)

The final momentum of man+boat is:

(m_man + m_boat)(v)

Set these two equal, then solve for "v".