Physics HW problem-I have an exam on Friday and want to understand how to do these problems.

Question

A fisherman has caught a very large, 5.0 kg fish from a dock that is 2.0 m above the water. He is using lightweight fishing line that will break under a tension of 57 N or more. He is eager to get the fish to the dock in the shortest possible time.

- If the fish is at rest at the water's surface, what's the least amount of time in which the fisherman can raise the fish to the dock without losing it?

Answer 1

Since the fish moves up, there must be a net upward force. This net upward force must be equal to the maximum tension of the fishing line minus the weight of the fish,

F_net = T – mg = 57 N – 5.0 kg x 9.8 m/s² = 8 N.

Now, F_net = ma_up  Solve for a_up = F_net / 5.0 kg = 1.6 m/s².

We now need to find the time it takes to move the fish from the surface of the water to the dock. We can use D = V₀t + ½ a_up t². V₀ = 0 m/s, so D = ½ a_up t². Solving for t, we get

t = √ 2 x D / a_up = √2 x 2.0 m / 1.6 m/s² = 1.6 s