Chinook salmon are able to move through water especially fast by jumping out of

Question

Chinook salmon are able to move through water especially fast 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 velocity 6.59 m/s at 48.1 degree above the horizontal, sails through the air a distance L before returning to the water, and then swims the same distance L underwater in a straight, horizontal line with velocity 3.70 m/s before jumping out again. Determine the average velocity of the fish for the entire process of jumping and swimming underwater, m/s Consider the time interval required to travel the entire distance of 2L. By what percentage is this time interval reduced by the jumping/swimming process compared with simply swimming underwater at 3.70 m/s?

Explanation / Answer

given: jumping out of water process: vix = 6.59cos48.1 viy = 6.59sin48.1 ax = 0 ay = -9.8 x = L underwater swimming process: vix = 3.70 viy = 0 ax = 0 ay = 0 x = L average velocity = total displacement / total time total displacement = 2L total time = ? time to complete entire jump: x = (vix)(t) + 0.5(a)(t^2) L = 6.59cos48.1(t) t = L/6.59cos48.1 t = .227L time to complete swim: x = (vix)(t) + 0.5(a)(t)^2 L = 3.70t t = .270L total time: t = .227L + .270L t = .497L average velocity = total displacement / total time average velocity = 2L/.497L average velocity = 4.02 m/s total time of jump + swim: t = .497L time to perform 2L distance by swimming only: x = (vix)(t) + (1/2)(ax)(t^2) 2L = 3.70t t = .541L percentage reduced = (.497L - .541L)/.541L * 100 percentage reduced = -8.05% percentage is reduced by 8.05% bol

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