Question

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?

Answer 1

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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

Answer 2

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

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