An oil tanker\'s engines have broken down, and the wind is blowing the tanker st

Question

An oil tanker's engines have broken down, and the wind is blowing the tanker straight toward a reef at a constant speed of 1.39 m/s (see figure below). When the tanker is 460 m from the reef, the wind dies down just as the engineer gets the engines going again. The rudder is stuck, so the only choice is to try to accelerate straight backward away from the reef. The mass of the tanker and cargo is 3.8 times 10^7 kg and the engines produce a net horizontal force of 7.7 times 10^4 N on the tanker. Will the ship hit the reef? You can ignore the retarding force of the water on the tanker's hull. Yes No If It does, will the oil be safe? The hull can withstand an impact at a speed of 0.197 m/s or less. Yes No The tanker does not hit the reef.

Explanation / Answer

force = mass * acceleration

7.7 * 10^4 = 3.8 * 10^7 * acceleration

acceleration = 0.002026 m/s^2

initial speed = 1.39 m/s

by third equation of motion

v^2 = u^2 + 2as

0 = 1.39^2 - 2 * 0.002026 * s

s = 476.826259 m

since the distance is more than 460 m the ship will hit the reef

again by third equation of motion

v^2 = 1.39^2 - 2 * 0.002026 * 460

v = 0.261 m/s

since the speed is more than the hull can withstand so,

the oil will not be safe

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