Question

A billiard ball is moving in the x-direction at 30.0 cm/s and strikes another billiard ball moving in the y-direction at 40.0 cm/s. As a result of the collision, the first ball moves at 50.0 cm/s, and the second ball stops. In what final direction does the first ball move?

Answer 1

To solve this problem it is necessary to apply the trigonometric ratios of the given velocity components.

If we make a graph of the velocity vectors in their respective velocities according to the given description we will have something similar to the attached graph.

The angle could be obtained from the components of the opposite leg and the adjacent leg so that

$tan\theta = \frac{x}{y}$

$\theta = tan^{-1}(\frac{x}{y})$

The opposite leg value (y) is 40cm / s and the adjacent leg (x) is 30cm / s

$\theta = tan^{-1}(\frac{30}{40})$

$\theta = 36.87\°$

Therefore the final direction that does the first ball is 36.87°