The leader is the weakest part of a fly-fishing line. A given leader can withsta

Question

The leader is the weakest part of a fly-fishing line. A given leader can withstand 19 N of force. A trout when caught will accelerate, taking advantage of slack in the line, and some trout are strong enough to snap the line. Assume that with the line taut and the rod unable to flex further, a 1.3 kg trout is just able to snap this leader. How much time would it take this trout to accelerate from rest to 5.0 m/s if it were free of the line? Note: Trout can reach speeds like this in this interval of time.

Explanation / Answer

For the trout to just break free of the line, it must be pulling with a force equal to the maximum capacity of the leader, which is 19 N. Once the trout breaks free, there is no more tension acting on it, only its own pull in the direction of motion. So we know that the force on the trout is 19 N once it breaks free. This force then causes an acceleration in the direction of motion, which determines how much time the trout needs to move from rest to 5.0 m/s

From Newton's Second Law and the equations of kinematics

(1) F = ma

(2) vf = vi +at

If we solve (1) for a and substitute this into (2), we get

vf = vi + t(F/m)

Finally, solving for t gives

t = [m(vf - vi)]/F = [(1.3 kg)(5.0 m/s)]/19 N = 0.342 s

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