   Chapter 3, Problem 50AP

Chapter
Section
Textbook Problem

Chinook salmon are able to move upstream faster by jumping out of the water periodically; this behavior is called porpoising. Suppose a salmon swimming in still water jumps out of the water with a speed of 6.26 m/s at an angle of 45°, sails through the air a distance L before returning to the water, and then swims a distance L underwater at a speed of 3.58 m/s before beginning another porpoising maneuver. Determine the average speed of the fish.

To determine
The average speed of the fish.

Explanation

The vertical component of the salmon’s velocity as it leaves water is,

v0y=v0sinθ

Here,

v0 is the initial velocity

θ is the angle with which the salmon jump

Substitute 6.26m/s for v0 and 45.0° for θ .

v0y=(6.26m/s)sin45.0°=4.43m/s

The vertical component of the salmon’s velocity as it returns to the water level is,

vy=v0y=4.43m/s

The time salmon is out of the water is,

t1=vyv0yay

Here,

vy is the vertical component of the velocity

v0y is the vertical component of the initial velocity

ay is the vertical acceleration

Substitute 4.43m/s for vy , 4.43m/s for v0y and 9.80m/s2 for ay .

t1=4.43m/s4.43m/s9.80m/s2=0.904s

The distance travelled horizontally during this time is,

L=v0xt1=(v0cosθ)t1

Substitute 6

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