Solve Math Problems: Find Functions Easily

[Mitza]

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.

 

[symbolipoint]

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]

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!

 

[symbolipoint]

I am glad my post helped. You must understand, most of the time, responding members will not give as thorough a solution as I did. Doing so as early in the topic as I just did and as thoroughly is a violation of the guidelines for giving homework help. (I guess the moderators did not catch me yet on this one.) We are supposed to help you think but make you do some or most of the work.

I still did not provide TO YOU the diagram or picture. This is something you should still try to make for yourself, as you should in other mathematical exercise problems.

 

[Mark44]

Doing so as early in the topic as I just did and as thoroughly is a violation of the guidelines for giving homework help.

And even more so when no effort has been shown by the OP...