CP? An oil tanker’s engines have broken down, and the wind is blowing the tanker straight toward a reef at a constant speed of 1.5 m/s (?Fig. P4.34?). When the tanker is 500 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 3.6 X 107 kg, and the engines produce a net horizontal force of 8.0 X 104 N on the tanker. Will the ship hit the reef? If it does, will the oil be safe? The hull can withstand an impact at a speed of 0.2 m/s or less. Ignore the retarding force of the water on the tanker’s hull.
Solution 38P Horizontal force F = 8.0 × 10 N 4 Mass of the tanker m = 3.6 × 10 kg 7 Acceleration of the tanker a = F/m 4 7 2 a = 8.0 × 10 N/3.6 × 10 m/s 3 2 a = 2.22 × 10 m/s Initial speed of the tanker is u = 1.50 m/s If the tanker has to stop, its final speed (v) will be zero. Let us now calculate the distance travelled by the tanker before it stops. Let S be the distance moved by the tanker. 2 2 From the equation, v = u 2aS 0 = 1.50 2 × 2.22 × 10 3 × S S = 506 m Since 506 m > 500 m, the tanker will hit the reef. Given that, the hull can withstand an impact at a speed of 0.2 m/s or less. Let us now calculate the speed of the tanker (v ) whfn it travels 500 m. v f2 = (1.5) 2 × 2.22 × 10 3× 500 v 2 = 2.25 2.22 f v f 0.173 m/s Therefore, when the tank hits the reef 500 m away, its speed will be 0.173 m/s which is lower than the impact speed of 0.2 m/s which the same can withstand. Therefore, the oil will be safe.