Thread: Finding an angle

A ship cruises forward at Vs=5 m/s relative to the water. On deck, a man walks diagonally toward the bow such that his path forms an angle theta = 22 degrees with a line perpendicular to the boat's direction of motion. He walks at Vm = 2 m/s relative to the boat



The speed he walks relative to the water is 5.749 m/s.

At what angle to his intended path does the man walk with respect to the water? Answer in degrees.


I was thinking maybe of using Tan-1(opposite/adjacent)
or some thing to that effect

It isn't 22 or 68 degrees

Hello, missashley!

A ship cruises forward at m/s relative to the water.
On deck, a man walks diagonally toward the bow such that his path forms
an angle with a line perpendicular to the boat's direction of motion.
He walks at m/s relative to the boat.

The speed he walks relative to the water is 5.749 m/s.

At what angle to his intended path does the man walk with respect to the water?
Answer in degrees.

Code:

      B        C
      * - - → *
      ↑      /
      |     /
      |    / 2
      |22*/
      |  /
      | /
      |/
      *
      A

In the right triangle, we have: .

Relative to the ship, he is walking 0.749 m/sec forward.

Since the ship is moving forward at 5 m/sec,
. . the man is moving forward at 5.749 m/sec (relative to the water).
(That's where they got that number.)

So relative to the water, his movement looks like this:

Code:

          5.749
      * - - - - - *
      |         /
      |       /
1.854 |     /
      |   /
      |θ/
      *

We have: .

Hence: .

Relative to the forward direction of the boat, his angle is about 17.9°.