Question

5. A porpoise jumps straight up and crashes back into the water at 8.9 m/s. The drag and

buoyancy forces of the water slow the porpoise down with an acceleration of -9.3 m/s-as the porpoise finally slows to a stop. Find the depth the porpoise reaches

Answer 1

Using the moment the porpoise re-enters the water as the origin, and the downward direction to be positive, it will reach a depth y after time t of

y = (8.9 m/s) t + 1/2 (- 9.3 m/s²) t²

with velocity v of

v = 8.9 m/s + (- 9.3 m/s²) t

Find the time it takes for the porpoise to come to a stop:

0 = 8.9 m/s + (- 9.3 m/s²) t

t = (8.9 m/s) / (9.3 m/s²)

t ≈ 0.96 s

After such time, its depth is

y = (8.9 m/s) (0.96 s) + 1/2 (- 9.3 m/s²) (0.96 s)²

y ≈ 4.3 m