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

Answer:

1. 19.24 mi/h

2. 9 degrees west of north

Step-by-step explanation:

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

$V^2=V_N^2+V_W^2\\V=\sqrt{3^2 +19^2}\\V=19.24\ mi/h$

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:

$tg(\theta) = \frac{V_W}{V_N} =\frac{3}{19}\\ \theta =8.97^o$

Her direction is approximately 9 degrees west of north.