A(trolley + child ) of total mass 200 kg is moving with a uniform speed of 36 km/h on a frictionless track. The child of mass 20 kg starts running on the trolley from one end to the other (10 m away ) with a speed of $10 m s^{- 1}$ relative to the trolley in the direction of the trolley's motion and jumps out of the trolley with the same relative velocity. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?

Open in App

Solution

Speed of trolley = 36 km/h , = 10 m/s
By momentum conservation of trolley before jump the boy (u).
Velocity of child w.r.t ground = 20 m/s
$200 \times 10 = 180 u + 20 \times 20 u = \frac{2000 - 400}{180} = \frac{1600}{180} u = \frac{160}{18} = \frac{80}{9}$
Time taken by boy to travel 10 m is 1 second.Then trolley
$\frac{80}{9 \times 1} \times 1 = 8.89 m$

Suggest Corrections

Similar questions

Q. A

(t r o l l e y + c h i l d)

of total mass

200 k g

is moving with a uniform speed of

36 k m / h

on a frictionless track. The child of mass

20 k g

starts running on the trolley from one end to the other

(10 m

away) with the speed of

10 m s^{- 1}

relative to the trolley in the direction of the trolley's motion and jumps out of the trolley with the same relative velocity. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?

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?

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 to 4 m/s relative to the trolley in a direction opposite to the trolley's 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?

A child is standing at one end of a long trolley moving with a speed v on a smooth horizontal track. If the child starts running towards the other end of the trolley with a speed u, the centre of mass of the system (trolley $+$ child) will move with a speed.

Q. A child is standing at one end of a long trolley moving with a speed 'v' on a smooth horizontal track. If the child starts running towards the other end of the trolley with a speed 'u', the centre of mass of the system (trolley + child) will move with a speed

Join BYJU'S Learning Program

Speed of trolley = 36 km/h , = 10 m/sBy momentum conservation of trolley before jump the boy (u).Velocity of child w.r.t ground = 20 m/s200×10=180u+20×20u=2000−400180=1600180u=16018=809Time taken by boy to travel 10 m is 1 second.Then trolley 809×1×1=8.89m