Two boys,each of mass m,are standing at the back of a flatbed trolley of mass 4m.the trolley is at rest on a frictionless horizontal surface.The boys jump off simultaneously at one of end of the trolley whith a horizontal velocity of 2m's.the trolley moves in the opposte direction.calculate the final velocity of the trolley

Use the law of conservation of momentum to solve this.

To calculate the final velocity of the trolley, we can use the principle of conservation of momentum. According to this principle, the total momentum before the boys jump off should be equal to the total momentum after they jump off.

Before the boys jump off, the total momentum of the system is given by the sum of the momenta of the boys and the trolley:

Total momentum before = (mass of boy 1 * velocity of boy 1) + (mass of boy 2 * velocity of boy 2) + (mass of trolley * velocity of trolley)

Since the boys are initially at rest on the trolley, their velocities are zero:

Total momentum before = (0 * 0) + (0 * 0) + (4m * velocity of trolley)

After the boys jump off, the total momentum of the system is given by the sum of the momenta of the boys and the trolley:

Total momentum after = (mass of boy 1 * velocity of boy 1) + (mass of boy 2 * velocity of boy 2) + (mass of trolley * velocity of trolley)

The boys jump off with a horizontal velocity of 2 m/s, so their velocities are:

velocity of boy 1 = velocity of boy 2 = 2 m/s

Substituting the values into the equation, we get:

Total momentum after = (m * 2 m/s) + (m * 2 m/s) + (4m * velocity of trolley)

According to the conservation of momentum principle, the total momentum before should be equal to the total momentum after:

Total momentum before = Total momentum after

(0 * 0) + (0 * 0) + (4m * velocity of trolley) = (m * 2 m/s) + (m * 2 m/s) + (4m * velocity of trolley)

Simplifying the equation, we have:

0 + 0 + (4m * velocity of trolley) = 2m + 2m + (4m * velocity of trolley)

0 = 4m

Since the mass cannot be zero, we find that the initial assumption that they have jumped off simultaneously at the one end is incorrect. There must be some time difference between when the first boy jumps off and when the second boy jumps off for the trolley to move.

Therefore, without more information, we cannot determine the final velocity of the trolley.