Question

a trolley of mass 200kg moves with uniform speed of 10m/s on a frictionless track.a child of mass 20kg runs on the trolley frm one end to another(10m)with a speed of 4m/s relative to the trolley in a direction opposite to its motion and jumps out of trolley.
what is the final speed of trolley?
how much has trhe trlley moved from the time the child begins to run?

Answer 1

consider the (trolley+child) system. It moves with a constant velocity of 10 m/s. Therefore, the momentum of the system=(220)*10=2200 kgm/s.
momentum of the trolley + momentum of the child=momentum of the (child + trolley) system
200*v1- 20*(4-v1)= 2200
200*v1-80+20v1=2200
220*v1=2280
v1=2280/220
v1=10.36 m/s.
second part- shift in centre of mass of the system
200*0+20*5/220-(200*0/200)=100/220=0.55m
i am not sure. check it out.

Answer 2

100/220=0.45m.
i am sorry , had made a mistake in the above answer

Answer 3

the 2nd part of answer is wrong.....we have to take 4m/s in the direction of trolley as relative speed of child and hence we get 19/4 seconds *10.36m/s

Answer 4

i have one doubt when you said momentum of the trolley + momentum of the child=momentum of the (child + trolley) system how is that the 2nd part is true to find velocity?

Answer 5

can u please specify ure doubt i dont understand war u are askin?

Answer 6

i mean i dont understand ure doubt

Answer 7

let mass of trolley be m1 and mass of child be m2
then here m1*v1+m2*v2=(m1+m2)V
how come?

Answer 8

oh!i get it een i feel that the 2nd part is wrong!

Answer 9

*even

Answer 10

i know the answers but logic doesnt make sense

Answer 11

this is a law that states that the total initial momentum is equal to total final momentum

Answer 12

okay but this eqn will give a state where V of truck and chilsd is same even though the velocity of child is different and finally it jumps out

Answer 13

but at the moment when they are together they can be considered as 1 body with 1 velocity......

Answer 14

they are together all the time starting from trucks motion and consider this.... a person sitting inside a train and a boy running across the train are considered to have the same velocity?

Answer 15

do u understand?

Answer 16

no practically think about this

Answer 17

ya it is possible!

Answer 18

ok' think of 2 football players they are running towards each other they each have a certain momentum now they collide and become 1 object now the momentum of that object is equal to the sum of the momentum of the 2 players

Answer 19

right 9th standard ncert book example!
well the players are not initially running on top of each other are they?>

Answer 20

no!and yeah 9th nert example i likd that example!

Answer 21

how did u get 19/4 . please clarify

Answer 22

and also please tell what u mean by the 2nd part and 1st part bcoz i think u are getting confused there

Answer 23

Few questions:
Q1. When the trolley was moving with 10m/s, was the boy moving w.r.t. trolley?
or is it like, when trolley was moving, the boy was at rest w.r.t. trolley and later on
he started his motion w.r.t. trolley?
Q2. When the boy jumped off, did his his velocity w.r.t. trolley remain constant just
before and after the jump?

Answer 24

first we consider the boy and truck to be moving with 10m/s
let mass of boy=m2 and mass of truck m1 respectively with corresponding velocities
initial momentum=(m1+m2)10
later when boy starts to run he imparts a new velocity to the truck let that be V with respect to a stationary observer
so final momentum is
(m1*V)+(m2*V-4)
as relative velocity is directed opposite to trucks new motion
initial momentum=final momentum
got the answer V=29.36m/s
LESSON LEARNT:WHEN AN OBJECT MOVES INSIDE THE TRUCK IT CHANGES THE TRUCKS VELOCITY ALSO JUST AS SOON THE BOY BEGINS TO MOVE and that is taken and data is given according to this imparted new velocity

as for the second part we know that the boys relative velocity is 4m/s opposite to trolleys direction of motion so we calculate the time taken for covering 10m by boy(10/4 seconds) and later we calculate the distance covered by trucks new velocity at this time distncfe=29.36*(10/4)

Answer 25

salini u have got it right.
there's a mistake in king's answer coz he considers vel of boy to be (4-v1)
which is supposed to be v1-4