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?

Hi, thank you for posting your question here at Brainy.

The path of the watercraft and the water current, when joined by a line forming a right angle would make a right triangle. From here, we can know the component in which it is along the same direction with the watercraft. Let's denote this as x.

x = 6 miles/h * cos 75 degrees
x = 1.55 miles/h

Thus, the actual speed = 70 + 1.55 = 71.55 miles/h

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Blacklash Blacklash · Answer 2 · 2019-07-16T13:52:17+02:00

Answer:

Actual speed = 73.18 m/s

Step-by-step explanation:

Let positive x axis represent east and positive y axis represent north.

Robin rides a personal watercraft 75° west of south at 70 miles/hour.

Velocity of personal watercraft = 70 miles/hour at 75° west of south

= 70 miles/hour at 15° south of west

= -70 cos 15 i + -70 sin 15 j

= -67.61 i - 18.12 j

The water current is moving 6 miles/hour at an angle of 75° south of west.

Velocity of water current = 6 miles/hour at 75° south of west

= 6 miles/hour at 75° south of west

= -6 cos 75 i + -6 sin 75 j

= -1.55 i - 5.80 j

Total velocity = -67.61 i - 18.12 j -1.55 i - 5.80 j = -69.16 i - 23.92 j

[tex]\texttt{Actual speed =}\sqrt{(-69.16)^2+(-23.92)^2}=73.18m/s[/tex]