Answer
(a) The fish could have a weight of 45 N (a mass of 4.6 kg).
(b) The fish could have a weight of 37 N (a mass of 3.8 kg).
(c) It is not possible to land a 15-lb trout because the fishing line would break.
Work Step by Step
(a) If the fish is pulled up at a constant speed, then the acceleration is zero, and the maximum tension of 45 N is equal to the weight of the heaviest possible fish which can be pulled up.
$mg = F_T = 45 ~N$
$m = \frac{45 ~N}{9.80 ~m/s^2} = 4.6 ~kg$
The heaviest fish which can be pulled up has a weight of 45 N (a mass of 4.6 kg).
(b) $ma = \sum F$
$ma = F_T - mg$
$m = \frac{F_T}{g+a} = \frac{45 ~N}{9.80 ~m/s^2 + 2.0 ~m/s^2} = 3.8 ~kg$
$mg = (3.8 ~kg)(9.80 ~m/s^2) = 37 ~N$
The heaviest fish which can be pulled up with an acceleration of $2.0 ~m/s^2$ has a weight of 37 N (a mass of 3.8 kg).
(c) $15 ~lbs \times 4.45 ~N/lb = 67 ~N$
Since 67 N > 45 N, it is not possible to land a 15-lb trout because the fishing line would break.
