0.180-kg stone rets on a frictionless, horizontal surface. a bullet of mass 7.50 g, traveling horizontally at 390 m/s, strikes the stone and rebounds horizontally at right angles to its original direction with a speed of 210 m/s.
(a) compute the magnitude and direction of the velocity of the stone after it is struck.

The magnitud of the velocity is

and the direccion:

degrees from the horizontal.

Explanation:

Fist we define our variables:

The letters i and j represent the direction of the movement, i in this case is the horizontal direction, and j is perpendicular to i.

velocities with sub-index 1 are the speeds before the crash, and with sub-index 2 are the velocities after the crash.

Using conservation of momentum:

Clearing for the velocity of the stone after the crash:

Substituting known values:

The magnitud of the velocity is :

and the direction:

this is -28.3 degrees from the +i direction or the horizontal direcction.

Note: i and j can also be seen as x and y axis.

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explanation: