A ship h eads out of port with a speed of 25 knots in a beraing of 84 degrees. if there is a current of water?

Question

A ship h eads out of port with a speed of 25 knots in a beraing of 84 degrees. if there is a current of water flowing due West with a speed of 4 knots; what is the ships true course as a bearing?

Answer 1

This is probably easier with a diagram... I made a picture for clarity:
http://teh.nab.googlepages.com/picture.PNG
Anyways, so you have a right-angled triangle with the hypotenuse of length 25, and other angles 84 and 6 degrees. On one of the edges (the east-west one, which should be next to the 6 degrees), part of it is 4. We can work out the edges with trig.

Sine 84 = b/25
0.99452 = b/25
l = 24.86305

Sine 6 = h/25
0.10452 = h/25
h = 2.61321

So the side lengths are 2.61, 24.86, and 25.

l+4 = b
l + 4 = 24.86305
l = 20.86305

Angle k is the new bearing:
Tan k = 20.86305 / 2.61321
k = Tan-1 (20.86305 / 2.61321)
k = 82.86057


It's speed is the hypotenuse of the smaller triangle.
l^2 + b^2 = s^2
20.86305^2 + 2.61321^2 = s^2
442.09562 = s^2
s = 21.02607

So the ship is heading out on a bearing of 82.86057 degrees, and traveling at 21.02607 knots!

(note: if your values aren't equal to my values, it's as I use more decimal places than you see)

Answer 2

for the reason that the two ships are vacationing on the comparable velocity, they might have coated the comparable distance whilst they are 150 miles aside. permit this equivalent distance = x miles Now, one deliver is x miles from commencing place to the north and the different is x miles from commencing place to the east. The positions of the ships and commencing place variety a appropriate triangle whose hypotenuse is 150 miles and the different 2 factors are x miles each and every. subsequently, by using Pythagorus theorem, x^2 + x^2 = 150 => x^2 = seventy 5 => x = ?(seventy 5) = 5?3 miles. to unravel word problems, represent the a number of given and unknown (to be discovered) variables. Then initiate translating the information situation interior certainly one of those mathematical equations and resolve the equations to discover the unknown.

Answer 3

21.026 knots bearing 82.861°.