Speed of two bodies that sticks together after collision

[coconut62]

Homework Statement

Two railway trucks of masses m and 3m move towards each other in opposite directions with speeds 2v and v respectively. These trucks collide and stick together after the collision. What is the speed of the trucks after the collision?

Homework Equations

Conservation of momentum: m1v1 + m2v2 = (m1+m2)Vtotal

The Attempt at a Solution

m(2v) + 3m(-v) = (m+3m)V

V= -4/v
∴ speed = 4/v

Answer given: 5v/4

Apparently they added the 2mv and 3mv together for the initial momentum. Is the book wrong or am I wrong?

 

[ehild]

Homework Statement

Two railway trucks of masses m and 3m move towards each other in opposite directions with speeds 2v and v respectively. These trucks collide and stick together after the collision. What is the speed of the trucks after the collision?

Homework Equations

Conservation of momentum: m1v1 + m2v2 = (m1+m2)Vtotal

The Attempt at a Solution

m(2v) + 3m(-v) = (m+3m)V

Correct so far.

V= -4/v
∴ speed = 4/v

Wrong, do it again.

Answer given: 5v/4

Apparently they added the 2mv and 3mv together for the initial momentum. Is the book wrong or am I wrong?

The book is wrong.


ehild

 

[coconut62]

From " m(2v) + 3m(-v) = (m+3m)V "

2mv -3mv = 4mV

-mv = 4mV

V= -v/4

Speed does not have a direction, so answer is v/4. Why wrong?

 

[ehild]

You wrote speed=4/v in the original post

ehild

 

[haruspex]

Answer given: 5v/4.

That would be the right answer if m had speed v and 3m had speed 2v. Are you sure you quoted the question correctly?

 

[coconut62]

Yes. I quoted it correctly.