152k views
0 votes
Robin rides a personal watercraft 75° west of south at 70 miles/hour. The water current is moving 6 miles/hour at an angle of 75° south of west. What is the actual speed (rounded to the nearest hundredth) of Robin's watercraft?

A.
71.19 miles/hour
B.
73.19 miles/hour
C.
75.12 miles/hour
D.
77.13 miles/hour

User Sameer K
by
6.1k points

1 Answer

4 votes

Answer:

B. 73.19 mi/hr

Explanation:

First we need to define the angles from a common reference. Robin's watercraft is moving 75° west of south, which is the same as 15° south of west. The river is flowing at 75° south of west.

The watercraft velocity relative to the water is:

wx = 70 cos 15° ≈ 67.615

wy = 70 sin 15° ≈ 18.117

The river's velocity is:

rx = 6 cos 75° ≈ 1.553

ry = 6 sin 75° ≈ 5.796

Robin's net velocity is:

vx = wx + rx ≈ 69.168

vy = wy + ry ≈ 23.913

The speed (magnitude of velocity) is:

v = √(vx² + vy²)

v ≈ √(69.168² + 23.913²)

v ≈ 73.19

User Rianna
by
5.8k points