Inelastic Collision At An Angle

[Saendy]

Two objects of mass M (= 1 kg) each travel with identical speed (|v1| = |v2| = 3 m/s) making an angle of θ relative to the x-axis. After they collide with each other, they travel as one object of mass 2M and with a velocity v3 (|v3| = 2 m/s) in the horizontal direction.

What is the value for angle θ in radians?

I tried m1 * v1 * cos(θ) + m2 * v2 * cos(θ) = mf * vf, but that was just a blind attempt to try something.

It's a practice exam question so I know the answer, but I want to know how to get there.

 

[SammyS]

Two objects of mass M (= 1 kg) each travel with identical speed (|v1| = |v2| = 3 m/s) making an angle of θ relative to the x-axis. After they collide with each other, they travel as one object of mass 2M and with a velocity v3 (|v3| = 2 m/s) in the horizontal direction.

What is the value for angle θ in radians?

I tried m1 * v1 * cos(θ) + m2 * v2 * cos(θ) = mf * vf, but that was just a blind attempt to try something.

It's a practice exam question so I know the answer, but I want to know how to get there.

Hello Saendy. Welcome to PF !

Use conservation of momentum.

What's the momentum of the system (total momentum) before the collision?

What's the momentum of the system after the collision?

 

[Saendy]

Hi Sammy, thanks for replying!

The total momentum before should be:

Pi = (m1 * v1) + (m2 * v2) = (3*1) + (3*1) = 6

The total momentum after should be:

Pf = (2m * vf) = (2*2) = 4

 

[SammyS]

Hi Sammy, thanks for replying!

The total momentum before should be:

Pi = (m1 * v1) + (m2 * v2) = (3*1) + (3*1) = 6

Don't forget v₁ andv₂ are vectors. Momentum is too.

The total momentum after should be:

Pf = (2m * vf) = (2*2) = 4