6. A killer whale can swim as fast as 15 m/s. Suppose a killer whale swims in

one direction at this speed for 8.0 s, makes a 90° turn, and continues

swimming in the new direction with the same speed as before. After a certain

time interval, the magnitude of the resultant displacement is 180.0 m.

Calculate the amount of time the whale swims after changing direction.

If possible I could use a step by step answer

8.9 s

Explanation:

First, the killer whale swims at 15 m/s for 8.0 s. The distance is:

15 m/s * 8.0 s = 120 m

Then, the killer whale turns 90° and swims at 15 m/s for t seconds. The distance is:

15 m/s * t s = 15t m

These two distances form the legs of a right triangle. The resultant displacement is the hypotenuse. So using Pythagorean theorem:

(180) ² = (120) ² + (15t) ²

32400 = 14400 + 225t²

18000 = 225t²

t² = 80

t = 8.9

The whale swims for 8.9 seconds after turning.