A 400.0-m-wide river flows from west to east at 30.0 m/min. Your boat moves at 1

Question

A 400.0-m-wide river flows from west to east at 30.0 m/min. Your boat moves at 100.0 m/min relative 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 , 75.0 m downstream from B .

A: Where on the north shore will you land if you point your boat perpendicular to the water current?

B: What distance will you have traveled, if you point your boat perpendicular to the water current?

C: That is, the direction of your boat will remain perpendicular to the direction of the water current for the entire crossing?

D: If you initially aim your boat directly toward point C and do not change that bearing relative to the shore, where on the north shore will you land? To reach point C at what bearing (angle north of west) must you aim your boat? "Bearing" means the direction of the boat with respect to the water, not the land. Again, you should imagine that you can only look at the water to determine your direction (and not use a compass, or look at features on shore to make corrections in the direction) and that this direction is maintained for the entire trip across the river?

E: Refer to part D. How long (t) will it take to cross the river?

F: Refer to part D. What distance (d, as measured by an observer on the ground) do you travel?

G: Refer to part D. What is the speed of your boat as measured by an observer standing on the river bank (v=|VbG|)?

Explanation / Answer

a) It will take 4 mins to get across the river. During that time the river will carry you downstream 120m. You will land 120 m East of B

b) Distance traveled is found using Pythagoras = (400^2 + 120^2) = 418 m

E) 4 minutes

f) 418 m

g) the observer will see you cove 418 m in 4 minutes, so your speed is 104.5 m/min

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