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 (angleϕ 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|)?

a. downstream is a location with respect to the direction of the flow of the river, in this case from west to east. the boat would drift towards the NE direction due to the direction of water current.

b. lets say it takes time t to travel across the river, the resultant speed of boat would be given as Rs= sqrt ( 100/min^2 + 30m/mins^2) = 104.4m/mins

distance traveled would be 104.4 *t

c. false, the direction of boat wouldnt remain perpendicular the entire crossing but would drift toward the NE bearing provided the driver doesnt change or steer the boat.

d. a. taking the definition of downstream in question (a), your boat would land at a point x downstream to c

b. to land at c boat must be inclined at an angle of -79.19 deg NE, given by using the width of river and the distance of b to c.

cosФ= 75/ 400

Ф= 79.19°NE to get to c you must position boat at an angle of -79.19 deg from your initial bearing.

e. speed = distance/ time, time = distance / speed.

aiming toward point c, speed of boat is the resultant speed of boat with respect to the speed of water, using Pythagoras also

speed= [tex]\sqrt{ 100^{2} + 30^{2} }[/tex] = 104m/mins

distance to move from point a to c is given also given by

distance = [tex]\sqrt{400^{2} + 75^{2} }[/tex]= 406.97m

time = 406.97/ 104.4 = 3.89mins...

f. on the ground the observer see the boat speed as 100m/min.

distance traveled is given by speed * time= 100 * 3.89= 389m

g. speed of boat observed would be 100m/min