A 400m wide river flows from west to east at 30 m/min. Your boat moves at 100 m/
ID: 1707933 • Letter: A
Question
A 400m wide river flows from west to east at 30 m/min. Your boat moves at 100 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 m downstream from B.So, I would like to know
a) Where on the north shore will you land if you point your boat perpendicular to the water current and what distance you'll have traveled. I know disctance means solving for "x," but I'm still not sure how to set it up.
b)if you initially aim you boat towards point C and do not change that bearing relative to the shore, where on the north shore will you land?
THANKS!
Explanation / Answer
A 400m wide river flows from west to east at 30 m/min. Your boat moves at 100 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 m downstream from B.
So, I would like to know
a) Where on the north shore will you land if you point your boat perpendicular to the water current and what distance you'll have traveled. I know disctance means solving for "x," but I'm still not sure how to set it up.
River velocity=30/1min=30/60=0.5m/sec
Boat velocity=100/min=100/60=5/3 m/sec
Time taken to cross the river=400/[5/3]=240sec
Now distance down the stream=240*0.5=120m
b)if you initially aim you boat towards point C and do not change that bearing relative to the shore, where on the north shore will you land?
when we aim towards the point C tan =75/400
S0 =10.61degree
Hence in this travel time taken to cross the river=400/[5/3 cos10.61]=244sec
So distance travelled down the stream=244*0.5=122m
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