Answer to Question #168534 in Physics for charles

Question

You are working as an expert witness for the defense of a container ship captain whose ship ran into a reef surrounding a Caribbean island. The captain is being charged with intentionally running the ship into the reef. In discovery, the following information has been presented, and attorneys on both sides have stipulated that the information is correct: The ship was traveling at 3.50 m/s toward the reef when a mechanical failure caused the rudder to jam in the straight-ahead position. At that point in time, the ship was 700 m from the reef. The wind was blowing directly toward the reef, and exerting a constant force of 8.00 ✕ 103 N on the boat in a direction toward the reef. The mass of the ship and its cargo was 6.00 ✕ 107 kg. During the preparation for the trial, the captain claims that without control of the direction of travel, the only choice he had was to put the engines in reverse at maximum power, such that the total force exerted by the frictional drag force of the water and the force of the water on the propellers was 1.23 ✕ 105 N in a direction away from the reef. From this information, construct a convincing argument that nothing the captain could do in this situation could have prevented the ship from striking the reef.

Answer 1

First, calculate the net force for the total force exerted by the frictional drag force of the water and the force of the water on the propellers F, and the force of the wind f:

$$F_\text{net}=F-f.$$

According to Newton's second law:

$$a=\frac{F_\text{net}}{m}=\frac{F-f}{m}$$

is the deceleration the captain could achieve for the ship.

Now use kinematic equations to calculate the distance required for the ship to stop from 3.5 m/s at this deceleration:

$$d=\frac{v^2}{2a}=\frac{mv^2}{2(F-f)}=3196\text{ m}.$$

Calculate the distance it would take to stop without the influence of the wind:

$$d=\frac{v^2}{2a}=\frac{mv^2}{2F}=2988\text{ m}.$$

Thus, even without the wind the captain could not prevent the accident.