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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 $\mathrm{m} / \mathrm{s}$ at an angle of $45^{\circ},$ 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 $\mathrm{m} / \mathrm{s}$ before beginning another porpoising maneuver. Determine the average speed of the fish.

$\overline { v } = 3.73 \mathrm { ms } ^ { - 1 }$

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Rutgers, The State University of New Jersey

Hope College

University of Sheffield

University of Winnipeg

this would be the trajectory of the salmon. We can say that t someone the time it takes from Port point A to point b t Step one. This would be equal in two times the initial velocity v times sign of data divided by G. And so we can solve and say t someone is equaling two times 6.26 meters per second time sign 45 degrees divided by 9.8 meters per second squared. And we have that tea someone his equaling point 9033 seconds. We then have t's up to this is equaling to be prime sign of data divided by G. What's again? This is gonna be equaling two times 3.58 meters per second sign off 45 degrees divided by 9.8 meters per second. Squared and T's up to is then found to be 0.516 seconds. And we can say that then keep these two values in mind because we're going to use this to find the average speed, and we can say that then solving for our someone the distance between point A and point B. This would be these V squared sine of tooth Ada divided by G. And we know that plate as 45 degrees. So two times 45 degrees is 90 degrees and then sign of 90 degrees is one. So this is equaling one. And so this would be equaling 6.26 meters per second quantity squared, divided by 9.8 meters per second squared. This is equaling 3.99 meters. Our sub two is gonna be eggs the exact same method and again fade as equaling 45 degrees. So it's simply the crime squared over G. And this is gonna be equaling 3.58 meters per second quantity squared, divided by 9.8 meters per second squared. This is equaling 1.3 meters. So the average speed or the average velocity in this case this would be the average speed. Because where are we are, um, were less concerned with direction and we're more concerned with the lengths traveled by the by the fish and again our someone rcep to only takes into account this horizontal distance. And so we can actually we're aren't concerned with with direction. However, we are calculating an average velocity because if we weren't to calculate the average speed, actually we'd have to take into account this arc here. So Speed actually accounts for the path traveled. Velocity only accounts for the initial point on the final point. So a to C And so our average velocity would be rather our someone plus arson too divided by t someone plus t's up to. So this is equaling 3.99 meters plus 1.3 meters, divided by 0.9033 seconds plus 0.516 seconds. And this is equaling 3.73 meters per second. This would be the average velocity for the fish from point A to point C. That is the end of the solution. Thank you for