e Xe rc i s e 3.1 2 Suppose the river is moving east at 5.00 km/h and the boat i
ID: 1533800 • Letter: E
Question
e Xe rc i s e 3.1 2 Suppose the river is moving east at 5.00 km/h and the boat is traveling 45.0° south of east with respect to Earth. Find (a) the speed of the boat with respect to Earth and (b) the speed of the boat with respect to the river if the boat’s heading in the water is 60.0° south of east. (See Fig. 3.25b.) You will have to solve two equations with two unknowns. (As an alternative, the law of sines can be used.)
the answers are (a) 16.7 km/h (b) 13.7 km/h
an explanation with drawings please
Explanation / Answer
If it is heading 45º S of E, then it has equal velocity components S and E.
Then Vsin60 = Vcos60 + 5 km/h
V(sin60 - cos60) = 5 km/h
0.366V = 5 km/h
V = 13.7 km/h (b) speed of boat w/r/t river
(a) V = (13.7km/h*cos60 + 5 km/h) i + 13.7km/h*sin60 j = 11.85 km/h i + 11.86 km/h j
mag V = ·(11.85² + 11.86²) km/h = 16.7 km/h
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