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

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

Answer 4

b) To express d as a function of t, we first need to understand the relationship between time and distance. We know that the ship is sailing at a constant speed of 35 km/h. This means that for every hour that passes, the ship will have traveled 35 km.

Since the ship passed the lighthouse at 11 am and we're measuring time elapsed since 11 am, we can say that t represents the time in hours. Therefore, the relationship between d (distance traveled) and t (time elapsed) can be expressed as:

d = 35t

c) To find k∘d, we need to substitute the expression for d in terms of t into the expression for k in terms of d that you provided in part a).

Recall that the equation for k in terms of d is given as:

k = √(d^2 + (10+x)^2)

Since we know that d = 35t, we can substitute this value into the equation for k:

k = √((35t)^2 + (10+x)^2)

k∘d = √((35t)^2 + (10+x)^2) * 35t

This function represents the product of the expressions for k and d. It is essentially finding the value of k multiplied by the value of d at any given time t. It represents a relationship between the distance from the lighthouse (k) and the distance traveled by the ship (d) at any given time (t).