Two asteroids collide at right angles and stick together; i.e, their initial vel

Question

Two asteroids collide at right angles and stick together; i.e, their initial velocities were perpendicular to each other (take A initially moving to the right and B initially moving up).

Use momentum conservation (make a complete Momentum Chart) to find the velocity (magnitude and direction with-respect-to the velocity asteroid A had before the collision) of the asteroids after the collision.

Relevant info

Before the collision, asteroid A (mass 1,000 kg) moved at 100 m/s, and asteroid B (mass 2,000 kg) moved at 80 m/s.

Explanation / Answer

Two asteroids collide at right angles and stick together.  A initially moving to the right and B initially moving up.

Before collision Momentum of A = 1000 * 100 = 105   in right direction

Before collision Momentum of B = 2000*80 = 1.6* 105 in upward direction.

After collision Mass of System = 1000 + 2000 = 3000 kg

Now Applying Momentum Conservation

Initial momentum in right direction = final momentum in right direction = 105 And

Initial momentum in upward direction = Final momentum in upward direction = 1.6*105

So Vx = 105 /3000 = 100/3 m/s

Vy =160/3 m/s      

Hence Velocity = (Vx 2 + Vy2)1/2 = 62.89 m/s [Magnitude ]

Direction :

And tan(angle from X axis) =   Vy /Vx = 1.6.

angle from X axis = 58 degree

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