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Calculus/Rate-time-distance problem

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Expert: - 9/18/2009


Question
A ship is moving at a speed of 40 km/h parallel to a straight shoreline. The ship is 4 km from shore and it passes a lighthouse at noon.
(a) Express the distance s between the lighthouse and the ship as a function of d, the distance the ship has traveled since noon.
s = f(d) =   

(b) Express d as a function of t, the time elapsed since noon.
d = g(t) =   

(c) Find f composed g.
(f  g)(t) =

Answer

Ship
Questioner: Sarah
Country: United States
Category: Calculus
Private: No
Subject: HELP! MATH!
Question: A ship is moving at a speed of 40 km/h parallel to a straight shoreline. The ship is 4 km from shore and it passes a lighthouse at noon.
(a) Express the distance s between the lighthouse and the ship as a function of d, the distance the ship has traveled since noon.
s = f(d) =   

(b) Express d as a function of t, the time elapsed since noon.
d = g(t) =   

(c) Find f composed g.
(f  g)(t) =


Hi, Sarah,

Since you didn't tell me what you already tried, I'll get you started.

I attached a diagram.  It is probably the same as you drew.  (You didn't draw a diagram?  There is no hope for you.)

a)  I think  d, s, 4  are the sides of a right triangle.  That should do it for  

s = a function of d.

b) Remember distance = rate * time, from elementary algebra?  That should do it for this.

c) Write  f( g(t)).  Then once you have found your g(t) [part b], substitute that into f() and simplify.

If you still have trouble, let me know and I'll see what I can do.

Paul Klarreich

Expertise

All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions. I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.

Experience

I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.

Education/Credentials
(See above.)

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