Jane plans to fly from Binghampton, New York, to Springfield, Massachusetts, about 280 km due east of Binghampton. She heads due east at 280 km/h for one hour but finds herself at Keene, which is 294 km from Binghampton in a direction 17.8 degrees north of due east. What was the wind velocity?
A) 14 km/h, E
B) 14 km/h, W
C) 14 km/h, N
D) 90 km/h, S
E) 90 km/h, N

Question

Quizplus · Accepted Answer

The wind caused Jane to deviate from her intended due east path to a path 17.8 degrees north of east. Given she ended up 294 km away in this direction after 1 hour, the wind's effect is perpendicular to her intended path, pushing her north. To find the wind's velocity, we can use trigonometry. The distance she was supposed to travel due east (280 km) and the actual distance traveled (294 km) form a right triangle, with the northward deviation as the opposite side. The angle given is 17.8 degrees north of east, which corresponds to the angle in the triangle. Using the sine function, sin(17.8°) = opposite/hypotenuse = northward deviation / 294 km. Solving for the northward deviation gives the wind's velocity northward, which is approximately 90 km/h, making the correct answer E, 90 km/h, N.

Jane Plans to Fly from Binghampton, New York, to Springfield