# Finding functions

Mitza
Member warned that some effort must be shown in homework questions
Homework Statement:
It's a three part problem

A ship is moving at a speed of 10 km/h parallel to a straight shoreline. The ship is 3 km from the shore and it passes a lighthouse at noon.

A. Let d be the distance (in km) that the ship has travelled since noon. Find the distance s between the lighthouse and the ship in terms of d. In other words, find a function f(d) such that s=f(d)

B. Express d as a function of time. In other words, find a function g(t) such that d=g(t)) where t is time elapsed (in hours) since noon.

C. Use composition to write down the distance between the lighthouse and the ship as a function of t.
Relevant Equations:
a^2+b^2=c^2 (maybe I'm not sure if this is what to use)
I really have no clue how to start this. I think I might have to use Pythagoras but I'm really not sure.

Homework Helper
Gold Member
Maybe you only need someone to sketch the right-triangle figure and label some parts for you. I did this on paper in just about 3 or 4 minutes.

Distance from ship to shore, 3 km;
Distance d ship travels in x hours, d=10x, because ship moves 10 km per hr;
Distance from lighthouse is hypotenuse. The right angle is where the ship is closest to light house at noon.

Correct, need use Pythagorean Theorem equation.
s^2=d^2+3^2
and you have figured that d=10x; so substitute and get
s^2=(10x)^2+3^2
and you can finish from here.

• Mitza
Mitza
Maybe you only need someone to sketch the right-triangle figure and label some parts for you. I did this on paper in just about 3 or 4 minutes.

Distance from ship to shore, 3 km;
Distance d ship travels in x hours, d=10x, because ship moves 10 km per hr;
Distance from lighthouse is hypotenuse. The right angle is where the ship is closest to light house at noon.

Correct, need use Pythagorean Theorem equation.
s^2=d^2+3^2
and you have figured that d=10x; so substitute and get
s^2=(10x)^2+3^2
and you can finish from here.
Okay thank you!

Homework Helper