You throw a basketball from a cliff to the ground. The ball has an initial velocity of 12 m/s in the horizontal direction. After 3.0 seconds, the ball has a velocity of -30.0 m/s in the y-direction. What is the direction of motion of the ball at time t= 3.0 s? (Hint: direction is related to the angle).

The direction of motion of the ball is approximately 68.199º below the +x semiaxis.

Explanation:

The ball has a two-dimension motion, to be exact, a parabolical motion, that is, a motion at constant velocity in the x-direction and free fall motion in the y-motion. Hence, the horizontal velocity of the basketball is 12 meters per second and its direction (), in sexagesimal degrees, is calculated by this trigonometrical expression:

(1)

Where:

- Horizontal velocity, in meters per second.

- Vertical velocity, in meters per second.

If we know that and , then the direction of motion of the ball is:

(below the +x semiaxis)

The direction of motion of the ball is approximately 68.199º below the +x semiaxis.

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