An explosion breaks a 26.0-kg object into three parts. the object is initially moving at a velocity of 30.0 m/s due west. part (1) has a mass m 1 = 4.90-kg and a velocity of 58.0 m/s due west. part (2) has a mass m 2 = 6.20-kg and a velocity of 72.0 m/s due south. what is the magnitude of the velocity of part (3)?

The magnitude of the velocity of part 3 is 46.60 m/s

Explanation:

We can solve this problem using conservation of linear momentum.

As there are no external forces in the horizontal direction, we know

So, the horizontal linear momentum is conserved.

Using the unit vector pointing west and the unit vector pointing south,  the initial momentum is

and the final momentum is

with velocities:

And, as the total mass is :

so, the third mass is :

but this must be equal to the initial momentum

so:

To find the magnitude, we just need to use the Pythagorean theorem