A 400.0- m -wide river flows from west to east at 30.0 m / m i n . Your boat mov

Question

A 400.0-m-wide river flows from west to east at 30.0 m/min. Your boat moves at 100m/minrelative to the water no matter which direction you point it. To cross this river, you start from a dock at point A on the south bank. There is a boat landing directly opposite at point B on the north bank, and also one at point C , 75.0mdownstream from B.

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A 400.0-m-wide river flows from west to east at 30.0 m/min. Your boat moves at 100m/minrelative to the water no matter which direction you point it. To cross this river, you start from a dock at point A on the south bank. There is a boat landing directly opposite at point B on the north bank, and also one at point C , 75.0mdownstream from B. To reach point C at what bearing must you aim your boat? Express your answer to three significant figures and include the appropriate units. l = on the west of point C I actually have the answer(see the following), but I am still confused and dont know what I should type in. My answer should not be in degree, but in meter.

Explanation / Answer

There are probably several ways to answer this. Basically you have to determine how long it will take the boat to travel across the river to the other shore. Once you know that, you can calculate how far the boat will move due to the river flow and add it to the vector that the boat moves from west to east.

1) Use pythagorean theorem a^2 + b^2 = c^2 where c is the hypotenuse of the triangle. The line from point A to point B is 400 m (the width of the river), the line from point B to point C is 75 m. (400)^2 (squared) + (75)^2 = c^2 (c is the distance from point A to Point C) Solve for this and you get 406.97 m. (c= square root of (160000 + 5625)) [alternatively, you could use trigonometry: Tangent = opposite/adjacent, so tangent of the angle at A = 75/400. Solving for angle A, you get 10.6 degrees. Then using angle A, Sin(10.6) = 75/c where c is the distance from point A to point C. c = 75/Sin(10.6) = 406.97 m]

2) Figure out how long it will take to cross the river and get to the other shore. If the boat moves at 100m/min and it has to travel 406.97m, then the time is 406.97/100 = 4.07 min (4.0697 min)

3) If there was no current in the river, the boat would end up at point C, 75m east of point B. (It would move 75 m to the east) There is a current, however, and the boat will be exposed to it for 4.07 minutes. The current is 30 m/min, so in 4.07 seconds, the boat will move an additional 30 x 4.07 = 122.1 m.

4) The boat will hit the shore 122.1 meters east of point C or 197.1 m east of point B (point B is 75 meters west of point C)

This would be a lot easier to solve if you aimed at point B to start with. Be sure the problem said point C.

b

..B----75m-----C

..|............../

..|4........../

a|0......../.........________________

..|0....../ c = / (400)^2 + (75)^2 = 406.97 m (this is supposed to be a square root sign)

..|....../......../

..|..../

..A./

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