A woman walks due west on the deck of a ship at 3 mi/h.

Question

A woman walks due west on the deck of a ship at 3 mi/h. The ship is moving north at a speed of 24 mi/h. Find the speed and direction of the woman relative to the surface of the water. (Round your answers to one decimal place.)

Answer 1

due west at 3 mph

due north at 24 mph

construct a right triangle

with hypotenuse = h

h^2 = w^2 + n^2

take the derivative with respect to time

2hh' = 2ww' +2nn'

divide by 2

hh' = ww' +nn'

solve for h' = her speed

h' = (3w +24n)/h

in 1 hour, w=3, n=24, h=sqr(9+24^2) = about 24.2

h' = (9+24^2)/24.2 = about 24.2 mph

direction is an angle = tan^-1(24/3) = 82.875 degrees or 172 7/8 degrees with the positive x axis

= 7 1/8 degrees NNW

she's going slightly faster than 24 mph with respect to the water surface

and slightly West of due North or about 352.9 degrees where North = 360 degrees