Question

Question 6.28 A trolley of mass 200 kg moves with a uniform speed of 36 km/h on a frictionless track. A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of 4 m s–1 relative to the trolley in a direction opposite to the its motion, and jumps out of the trolley. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?

Chapter Work, Energy And Power Page 138

Answer 1

Hey there !!!!!

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Mass of trolley (M) =200kg

Speed of trolley = 36kmph= 36*5/18 = 10m/s

Mass of boy (M₁) = 20kg

Initial Momentum = (Mass of trolley+Mass of boy)velocity of trolley

                            =(M+M₁)v

                            =(200+20)10=2200kgm/s

If final velocity of trolley wrt to ground is  v₁

Final velocity of boy would be v₁₁= v₁-4

So Final Momentum is :

 = Mass of trolley*Final velocity+ Mass of Boy*final vleocity

 = 200*v₁+ 20v₁-80

 = 220v₁-80

Now using law of conservation of momentum

Initial Momentum = Final Momentum

2200 = 200v₁-80

2280=200v₁

v₁ = 10.3 m/s

So final velocity of trolley = 10.3 m/s

Distance moved by trolley when boy starts to run = v₁*t

t = distance covered by boy/ speed = 10/ 4 =2.5s

Distance moved by trolley = 10.3*2.5 = 25.75m 

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Hope this helped you...................

Answer 2

Hy


distance travel by trolley =25.9m

velocity of trolley against ground =10.36m/s

speed of boy=2.5m/s

hope it help