Question

Im stuck on this question of b) and c),i already got a) which is as it can be the distance k can be given as k=squareroot d^2+(10+x)^2

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.


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?

Answer 1

what is that x about?
d is distance traveled
k is hypotenuse
10 , not (10+x) is original distance leg

k = sqrt (d^2 + 100)

d = v t

Is c) the dot product of k and d? I do not understand your notation
If it is k dot d
then that is |k| |d| cos angle between path direction and angle between path and bearing of lighthouse

k dot d =sqrt(d^2+100) d cos T
but
cos T = -d/sqrt(d^2 + 100)
so
k dot d = - d^2
It just means that the component of k in the direction of d is just -d. , not news if you drew a good diagram :)

Answer 2

I think this is suppose to be composite function

Answer 3

so d = v t