Two persons A and B, each of mass in are standing at the two ends of rail-road car of mass M. The person A jumps to the left with a horizontal speed u with respect to the car. Thereafter, the person B jumps to the right, again with the same horizontal speed u with respect to the car. Find the velocity of the car after both the persons have jumped off.

Open in App

Solution

Speed of the cart when first person (A) jumped
So, according to momentum conservation
$m u = (M + m) v v = \frac{m u}{M + m}$
Now the cart is moving with velocity v towards right and person B jumps
Again
$P_{i} = (m + M) (\frac{m u}{M + m}) P_{f} = m u + M (v) \Rightarrow m u + M (v) = m u v = 0$

Suggest Corrections

Similar questions

Q. Two persons each of mass m are standing at the two extremes of a railroad ear of mass

M

resting on a smooth track. The person on left jumps to the left with a horizontal speed

u

with respect to the state of the car before the jump. Thereafter, the other person jumps to the right, again with the same horizontal speed

u

with respect to the state of the car before his jump. Find the velocity of the car after both the persons have jumped off.

Two persons each of mass m are standing at the two extremes of a railroad car of mass M resting on a smooth track ,the given below figure.The person on left jumps to the left with a horizontal speed u with respect to the state of the cat before the jump.Thereafter,the other person jumps to the right,again with the same horizontal speed u with respect to the state of the car before his jump.Find the velocity of the car after both the persons have jumped off.

Two persons each of mass m are standing at the two extremes of a railroad car of mass M resting on a smooth track (figure). The person on left jumps to the left with a horizontal speed u with respect to the state of the car before the jump. Therefore, the other person jumps to the right, again with the same horizontal speed u with respect to the state of the car before his jump. Find the velocity of the car after both the persons have jumped off.

Q. Two person each of mass

m

a r e s t a n d i n g a t t h e t w o e x t r e m e s o f a r a i l r o a d c a r o f m a s s l e f t

r e s t i n g o n a s m o o t h t r a c k . T h e p e r s o n o n t h e l e f t j u m p s t o w i t h a v e l o c i t y

u$. Find the velocity of the train when both the person have jumped off.

Q. A flat car of mass

M

is at rest on a frictionless floor with a child of mass

m

standing at its edge. If child jumps off from the car towards right with an initial velocity

u

with respect to the car, find the velocity of the car after its jump.

Join BYJU'S Learning Program

Speed of the cart when first person (A) jumpedSo, according to momentum conservationmu=(M+m)vv=muM+mNow the cart is moving with velocity v towards right and person B jumpsAgainPi=(m+M)(muM+m)Pf=mu+M(v)⇒mu+M(v)=muv=0

Speed of the cart when first person (A) jumped
So, according to momentum conservation
$m u = (M + m) v v = \frac{m u}{M + m}$
Now the cart is moving with velocity v towards right and person B jumps
Again
$P_{i} = (m + M) (\frac{m u}{M + m}) P_{f} = m u + M (v) \Rightarrow m u + M (v) = m u v = 0$