I got A and B but i need C
Suppose a ship is sailing at a rate of 35km/h parellel to a straight shoreline. The ship is 10km from shore when it passes a lighthouse at 11am.
Question 6
a)
Let k be the distance between the lighthouse and the ship. Let d be the distance from the ship has travelled since 11am. Express k as a function of d. Please include a diagram.
b)
Express d as a function of t, the time elapsed since 11am.
c)
Find k∘d . What does this function represent?
To answer these questions, let's break it down step by step:
a) Let's begin by creating a diagram to visualize the situation. Draw a straight line to represent the shoreline and a point to represent the lighthouse. Label the distance between the lighthouse and the ship as "k" and the distance the ship has traveled as "d," as shown here:
Ship --> *_________* Lighthouse
We know that the ship and the lighthouse are parallel, so the distance between them remains constant throughout. Since the ship starts 10km from the shore when passing the lighthouse, this forms a right triangle. Using the Pythagorean theorem, we can express "k" as a function of "d":
k^2 + d^2 = 10^2
b) To express "d" as a function of time "t," we need to relate the ship's speed to the distance it has traveled. Since the ship is traveling at a constant speed of 35km/h, we can use the formula:
d = r * t
where "r" represents the ship's rate or speed (35km/h) and "t" represents the time elapsed since 11am.
c) To find the composition of the functions k∘d, we need to substitute the expression for "d" obtained in part b) into the equation from part a) to get a single function, k∘d.
Using the expression for "d" from part b) in the Pythagorean theorem equation from part a), we get:
k^2 + (r * t)^2 = 10^2
Simplifying this equation will give us the function k∘d, which represents the distance between the ship and the lighthouse as a function of the time elapsed since 11am.
Overall, the steps to solve these questions involve creating a diagram to visualize the situation, using relevant formulas, and solving equations to express the required functions.