Question

Woman walks due west on the deck of a ship at 3 mi/h. The ship is moving north at a speed of 19 mi/h. Find the speed and direction of the woman relative to the surface of the water. (Round your answers to one decimal place.)

1.speed: 19.24 mi/h Correct: Your answer is correct.
2.direction: N ?

Answer 1

1. 19.24 mi/h

2. 9 degrees west of north

Explanation:

The speed at which the woman moves relative to the surface of the water is given by:

`V^2=V_N^2+V_W^2\\V=√(3^2 +19^2)\\V=19.24\ mi/h`

Her relative velocity is 19.24 mi/h.

The angle at which she travels west of north has a tangent value equal to the western velocity divided by the northern velocity:

`tg(\theta) = (V_W)/(V_N) =(3)/(19)\\ \theta =8.97^o`

Her direction is approximately 9 degrees west of north.