Applying the force on a stationary trolley of mass 12 kg gives it a speed of 4 meters per second in 2 seconds. Then the trolley moves at the same speed. What is the velocity of the trolley while moving at the same speed?
Answers
Explanation:
Solution
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Mass of the trolley, M=200kg
Speed of the trolley, v=36km/h=10m/s
Mass of the boy, m=20kg
Initial momentum of the system of the boy and the trolley
=(M+m)v
=(200+20)×10
=2200kg m/s
Let v
′
be the final velocity of the trolley with respect to the ground.
Final velocity of the boy with respect to the ground =v
′
−4
Final momentum =Mv
′
+m(v
′
−4)
=200v
′
+20v
′
−80
From the conservation of linear momentum:
Initial momentum= Final momentum
2200=220v
′
−80
∴ v
′
=2280/220=10.36m/s
Length of the trolley, l=10m
Speed of the boy, v
′′
=4m/s
Time taken by the boy to run, t=10/4=2.5s
∴ Distance moved by the trolley =v
′′
×t= 10.36×2.5=25.9m