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 110 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 (Figure 1) . 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? c)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? d)To reach point C at what bearing must you aim your boat? e)How long will it take to cross the river? f)What distance do you travel? g)What is the speed of your boat as measured by an observer standing on the river bank?

Explanation / Answer

a) Time to cross river = (400/110) = 3.64 mins. In 3.64 mins., you are carried (30 x 3.64) = 109.2 m. downstream.

(b)  Distance traveled is found using Pythagoras = (400^2 + 109.2^2) = 414.6 m

(d) you only need to travel downstream 75 metres.So you need to point the boat as if to land (109.2 - 75) = 34.2 metres upstream (if NO current).
Point angle = arctan (34.2/400) = 4.89 degrees upstream.
e) Time to cross = 3.64 min/(cos4.89) = 3.63 mins.
f) Distance = sqrt. (400^2 + 75^2) = 406.97 metres. (note use of distance from B to C)
g) Relative to the observer, you have travelled 406.97 metres, in a time of 3.63 mins.
Speed is (406.97/3.63) = 112.11 m/min.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.