SOLUTION: One day visibility was limited to 1700m. Ship Blue was travelling west on a parallel course to Ship White, travelling east. The courses are 800m apart. Blue ship's velocity is 8 km

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Question 1104907: One day visibility was limited to 1700m. Ship Blue was travelling west on a parallel course to Ship White, travelling east. The courses are 800m apart. Blue ship's velocity is 8 km/h. If the ships were in sight of each other for 15 mins, what's the velocity, in km/h, of white ship?
Answer by ankor@dixie-net.com(22740) (Show Source):
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One day visibility was limited to 1700m.
Ship Blue was travelling west on a parallel course to Ship White, travelling east.
The courses are 800m apart.
Blue ship's velocity is 8 km/h.
If the ships were in sight of each other for 15 mins, what's the velocity, in km/h, of white ship?
:
let s = the white ship's velocity
then
(s+8) = the relative speed between the two ships
Assume the blue ship is stationary
:
We can draw this scenario as a scalene triangle. The height is 800 m
The Blue ship at the apex of the two equal sides which are 1700 m
The third side is the distance the ships are in sight of each other.
The triangle is made up of two right triangles which we can solve.
Find the equal angle (A) using the sine
sin(A) =
A = 28.07 degrees
Find the third side, using the cosine of 28.07
This will be half the distance (x) that they are in sight of each other
cos(28.07) =
x = 1500 meters
the distance they are in sight 2(1500) = 3000 meter which is 3 km
Given they were in sight of each other for 15 min which is hrs
Use a time equation to find the speed of the white ship
=
s + 8 = 3(4)
s + 8 = 12
s = 12 - 8
s = 4 km/hr is the speed of the white ship