Leona and Liam are standing on opposite banks of a river, which we can treat as

Question

Leona and Liam are standing on opposite banks of a river, which we can treat as having parallel banks separated by a distance of 130. m. Leona is on the east side of the river with her motorized model plane, while Liam is directly across the river from her, on the west side.

(a) Leona's plane travels at a constant speed of 5.60 m/s relative to still air. But on this particular day, the wind is blowing at a steady velocity of 3.40 m/s in an easterly direction, parallel to the river banks. Leona points the plane directly at Liam, but the wind blows it off course. When it reaches the far side of the river, how far is it from Liam?


(b) Liam retrieves the plane on the west side, and brings it back to his initial spot, directly across from Leona. Knowing some physics, Liam calculates at exactly what angle she should point the plane so that it ends up right at Leona (the wind is still blowing). What is this angle, measured from the straight line connecting Liam and Leona?


(c) How long does this particular trip across the river take?

Explanation / Answer

angle = arctan (3.4/5.6) = 31.26 degr distance= 130tan31.26 = 78.88m

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