Question

A Chinook salmon has a maximum underwater speed of 3.58 m/s, but it can jump out of water with a speed of 6.26 m/s. To move upstream past a waterfall, the salmon does not need to jump to the top of the fall, but only to a point in the fall where the water speed is less than 3.58 m/s; it can then swim up the fall for the remaining distance. Because the salmon must make forward progress in the water, let's assume it can swim to the top if the water speed is 3.00 m/s.

(a) If water has a speed of 2.07 m/s as it passes over a ledge, how far below the ledge will the water be moving with a speed of 3.00 m/s? (Note that water undergoes projectile motion once it leaves the ledge. The water's velocity is initially horizontal as it passes over the ledge. Enter the magnitude of the distance only.)

_____ m

(b) If the salmon is able to jump vertically upward from the base of the fall, what is the maximum height of waterfall that the salmon can clear?

_____ m

Answer 1

the water velocity increase is due to the change in gravitational potential energy

1/2 m 3.00^2 - 1/2 m 2.07^2 = m g h

3.00^2 - 2.07^2 = 2 g h


the kinetic energy of the jump is converted to gravitational potential energy

6.26^2 = 2 g h

the max waterfall is the sum of the two heights