# Math Help - Unsure how to tackle this problem.

1. ## Unsure how to tackle this problem.

Hi all I was wondering if anyone could point me in the right direction with this problem.

lighthouse L located at (90, -30) equation of the line of travel of the boat is $y=-\frac{1}{3}x+33\frac{1}{3}$

Let d kilometres be the distance between the location of the boat at parameter value t and the lighthouse L. Find an expression for d^2 in terms of t.

2. ## Re: Unsure how to tackle this problem.

You need to know how the boat is traveling along the line: uniformly or not, its speed, its location at t = 0.

3. ## Re: Unsure how to tackle this problem.

The boat is traveling in a striaght line
Its location at t=0 is (-200,100) and t=1 is (400,-100)
It is travelling at a constant speed of 4.8kph

4. ## Re: Unsure how to tackle this problem.

We have $x(t)-x(0)=t(x(1)-x(0))$ and similarly for y(t), from which you can find x(t), y(t) and (using the Pythagorean theorem) the distance between (x(t), y(t)) and L. Now, this distance is expressed in the units of the coordinate plane, which apparently are different from kilometers. You can find the distance between (x(0), y(0)) and (x(1), y(1)), which should equal 4.8 km assuming time is expressed in hours. From there you get a relationship between plane units and km.