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
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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:
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1.854 | /
We have: .
Relative to the forward direction of the boat, his angle is about 17.9°.