a man of 50kg is standing on one end on a boat of length 25m and mass 200 kg .if he starts running and when he reaches the other end ,he has a velocity 2m/s with respect to the boat .the final velocity of the boat is?
according to law of conservation of linear momentum
m1u1+m2u2=m1v1+m2v2
velocity of man with respect to man =Vm-Vb
2=Vm-Vb
therefore ,iniitally at rest so before =o
0=200Vb+100+50Vb
250Vb= -100
Vb= -2/5
To find the final velocity of the boat, we can apply the principle of conservation of momentum.
The total momentum before the man starts running is equal to the total momentum after he reaches the other end of the boat.
Before the man starts running, the initial momentum of the system is zero because both the man and the boat are at rest.
After the man reaches the other end with a velocity of 2 m/s with respect to the boat, we can calculate the change in momentum of the man using the formula:
Change in momentum = mass × change in velocity
Since the man's mass is 50 kg and his initial velocity is 0 m/s, the change in momentum of the man is:
Change in momentum of the man = 50 kg × 2 m/s = 100 kg·m/s
According to the principle of conservation of momentum, the change in momentum of the man must be equal in magnitude but opposite in direction to the change in momentum of the boat. Therefore, the change in momentum of the boat is -100 kg·m/s.
Now, we can calculate the final velocity of the boat using the formula:
Change in momentum = mass × change in velocity
Since the mass of the boat is 200 kg, the change in velocity of the boat is:
-100 kg·m/s = 200 kg × change in velocity
Solving for the change in velocity gives us:
change in velocity = -100 kg·m/s / 200 kg = -0.5 m/s
Therefore, the final velocity of the boat is -0.5 m/s. The negative sign indicates that the boat moves in the opposite direction of the man's motion, which is expected since the man's running exerts a backward force on the boat.
Total momentum (relative to land) must remain zero. Let V be the final boat velocity (positive backwards). The man's final velocity with respect to land will be (V -2)m/s.
200*V + 25*(V-2) = 0
175 V = 50
V = 0.286 m/s