Q: A boomerang travels 500 meters in a southward direction over the course of 90 seconds. The boomerang then makes an abrupt turn eastward and travels 300 meters in 60 seconds. What is the average velocity of the boomerang?
A: In a previous problem, the average speed of an object was determined. Speed is a scalar quantity, meaning that it possesses magnitude only. To determine average speed, the total distance traveled by an object is divided by the total time of travel.
Conversely, velocity is a vector quantity; it possesses both magnitude and direction. The net velocity of an object is determined by dividing its net displacement by the total time of travel. If an object travels from a starting point with a constant velocity and returns after some unit of time transpires, its net velocity will be zero.
The boomerang’s route of travel includes a right-angle turn. This enables us to use the Pythagorean Theorem to determine its net displacement:
a2 + b2 = c2
The “ a “ and “ b “ sides of the triangle above are ( 500 m ) and ( 300 m ), respectively. The unknown ( ? ) side is the hypotenuse of the right triangle. It’s value represents the net displacement of the boomerang after 150 seconds of travel. Substitution into the Pythagorean Theorem equation enables the unknown value to be solved:
( 500 m )2 + ( 300 m )2 = ?2
250,000 m2 + 90,000 m2 = ?2
340,000 m2 = ?2
? = 583 m
Thus, the magnitude of the boomerang’s average velocity is as follows:
( 583 m / 150 s ) = 3.89 m/s
The net direction of the boomerang’s velocity is southeast, even though its instantaneous direction is eastward.
RENAISSANCE PHYSICS 