To reach its intended destination on time a cruise ship needs to travel north at 70 mph. However, it is travelling in the Gulf of Mexico where there is a Gulf Stream current of 12 mph in the direction S25oE. At what speed and direction does the captain need to aim the boat so that the result takes them due north at the required 70 mph

speed is 81.03 mph

direction is N 3.58 W

Explanation:

given data

travel north = 70 mph

Stream current = 12 mph

direction = S 25° E

result due north = 70 mph

to find out

speed and direction

solution

we will get component of resultant that is

v cosθ and v sinθ

so

(12cos295, 12 sin295) at (0, 70)

as that we can say

v sinθ + 12sin295 = 70 ... 1

v cosθ + 12 cos295 = 0 ... 2

so

vcosθ = - 5.0714

vsinθ = 80.8756

now by ratio

cosθ / sinθ = - 5.0714 / 80.8756

cot θ = - 0.0627

θ = 93.58

so direction is N 3.58 W

and

we know

vcosθ = - 12cos295

v = - 12cos295 / cos (93.58)

v = 81.03 mph

so speed is 81.03 mph