A man of mass 50kg is walking on a long wooden board of mass 200 kg. The wooden board is initially at rest on a frictionless ice surface. If the man walks with a velocity 1m/s in the positive x direction relative to the wooden board,find the velocity of the board in m/s?

To find the velocity of the board, we can apply the principle of conservation of momentum. In this case, since there are no external forces acting on the system, the total momentum before and after the man starts walking should remain the same.

The initial momentum of the system is zero since both the man and the board are at rest. The final momentum of the system will also be zero since the man's velocity is relative to the board.

Let's assume the velocity of the board in the positive x-direction is "v" m/s. The man's initial velocity relative to the board is 0 m/s, and when he starts walking with a velocity of 1 m/s in the positive x-direction, the velocity of the board will become "v + 1" m/s.

Using the conservation of momentum:

(initial momentum of man) + (initial momentum of board) = (final momentum of man) + (final momentum of board)

(0 kg * 0 m/s) + (200 kg * 0 m/s) = (50 kg * 1 m/s) + (200 kg * (v + 1) m/s)

0 = 50 kg * 1 m/s + 200 kg * (v + 1) m/s

0 = 50 kg + 200 kg * (v + 1) m/s

Solving for "v":

200 kg * (v + 1) = -50 kg

(v + 1) = -50 kg / (200 kg)

(v + 1) = -0.25

v = -0.25 - 1

v = -1.25 m/s

Therefore, the velocity of the board is -1.25 m/s in the positive x-direction.

To find the velocity of the board, we can use the principle of conservation of momentum.

The total momentum of the system (man + board) is conserved before and after the man starts walking.

Before the man starts walking, both the man and the board are at rest, so the total momentum is zero.

After the man starts walking, the total momentum should still be zero.

Let's define the positive x-direction as the direction the man is walking. Since the man is walking in the positive x-direction relative to the board, when we consider the momentum of the man, it will be positive. On the other hand, the momentum of the board will be negative, as it moves in the opposite direction.

The momentum of an object is given by the product of its mass and velocity.

Let's denote the velocity of the board as Vb.

According to the conservation of momentum, we have:

(mass of the man × velocity of the man) + (mass of the board × velocity of the board) = 0

(50 kg × 1 m/s) + (200 kg × Vb) = 0

50 kg + 200 kg × Vb = 0

200 kg × Vb = -50 kg

Vb = -50 kg / 200 kg

Vb = -0.25 m/s

Therefore, the velocity of the board is -0.25 m/s. The negative sign indicates that the board is moving in the opposite direction (negative x-direction) compared to the man.