Newton's Law of Motion for a Straight Line Motion

1. Oct 16, 2008

!!!

1. The problem statement, all variables and given/known data
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. 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 104N 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. You can ignore the retarding force of the water on the tanker's hull.

2. Relevant equations
F = ma
vx = v0x + axt
x = x0 + v0xt + 1/2 axt2
vx2= v0x2 + 2ax(x-x0)
x - x0 = (v0x + vx / 2)t

3. The attempt at a solution
I don't exactly know what to do first, so I first found the acceleration of the ship's engines.
a = f/m = 8.0 x 104N / 3.6 x 107 kg = 2.22 x 103 m/s2

Then I tried to find the time it takes for the ship to hit the reef:
vx = v0x + axt
1.5 = 0 + (2.22 x 103)(t)
t = 6.757 x 10-4 s.

And plugged it into the distance traveled:
x = x0 + v0xt + 1/2 axt2
x = 0 + 0 + 1/2 (2.22 x 103)(6.757 x 10-4)2
x = 5.02 x 10-4 m.

The book's answer said that it's 506 m so the ship will hit the reef, and the speed at which the ship hits the reef is 0.17 m/s, so the oil should be safe.
But I don't know how to get to the correct answers. :(

2. Oct 17, 2008

CompuChip

Don't you think that a distance of 10^{-4} meter and a time of 10^{-4} seconds is a bit unrealistic? :)

3. Oct 17, 2008

!!!

Okay, so I calculated the ship's engine's acceleration again:
a = f/m = 8.0 x 104N / 3.6 x 107 kg = 2.22222 x 10-3 m/s2

Then I tried to find the time it takes for the ship to hit the reef:
vx = v0x + axt
1.5 = 0 + (2.22222 x 10-3)(t)
t = 675s.

And plugged it into the distance traveled:
x = x0 + v0xt + 1/2 axt2
x = 0 + 0 + 1/2 (2.22 x 10-3)(675)2
x = 505.74375 = 506 m.
Oh, thank you, guys, for correcting my miscalculation.

And if I find the speed to determine if the hull can withstand its impact or not?
vx = v0x + axt
vx = 0 + 2.22222 x 10-3(675)
v = 1.5 m/s
I don't know how to get 0.17 m/s ...

4. Oct 17, 2008

DeShark

This is the time it takes for the ship to stop, not for it to hit the reef.

You found the right distance and determined that it will hit the reef.
Now you want the speed after it's travelled a certain distance(500m)... you want $${v_x}^2= v_{0x}^2 + 2a_x(x-x_0)$$

Make sure you pick the right distances and forumlae!

Last edited: Oct 17, 2008
5. Oct 17, 2008

CompuChip

Why did you take v_0 to be zero? Also, you are using the wrong time. Think careful about what the parameters mean before you plug them in!