Kinematics Problem Help (accident-avoidance systems for oil tankers)

[Civil_Disobedient]

Homework Statement

Because of your technical background, you have been given a job as a student assistant in a university research laboratory that has been investigating possible accident-avoidance systems for oil tankers. Your group is concerned about oil spills in the North Atlantic caused by a super tanker running into an iceberg. The group has been developing a new type of forward-looking radar which can detect large icebergs. They are concerned about its rather short range of 2 miles. Your research director has told you that the time taken by the radar signal to travel from the ship to the iceberg is negligible. However, it takes the on-board computer 5 minutes to process the signal. Unfortunately, the super tankers are such huge ships that it takes a long time to turn them. Your job is to determine how much time would be available to turn the tanker to avoid a collision once the tanker detects an iceberg. A typical sailing speed for super tankers during the winter on the North Atlantic is about 15 mph. Assume that the tanker is heading directly at an iceberg that is drifting at 5 mph in the same direction that the tanker is going.

(Just copied the problem and bolded the useful stuff)

Homework Equations

X = Xo + volt + (1/2)at^2
X = Xo + volt

The Attempt at a Solution

Tanker variables: Xo = 0, Vo = 15
Tanker equation: X=volt (because Xo and acceleration are 0, no (0.5)at^2) so X = 15t

Iceberg variables: Xo = 2, Vo = 5
Iceberg equation: X = Xo + volt (because acceleration is 0, no (0.5)at^2) so X = 2 + 5t
Using algebra, X = 2 + 5t simplifies to 5t = X-2

Set X = 15t (Tanker) and 5t = X - 2 (Iceberg) equal to each other.
5t = 15t - 2
5t - 15t = -2
-10t = -2
t = 2/10 hours
60 minutes in an hour * 2/10 = 12 minutes
12 minutes - 5 minutes (because it takes 5 minutes to detect the iceberg) = 7 minutes

Wanted to check to see if I did it right and used a proper method. Yes, I'm aware this is probably duck soup but I'm only taking an introductory physics course atm.

 

[kuruman]

Hi Civil_Disobedient and welcome to PF.

Your solution looks OK.