The water in a river flows uniformly at a constant speed of 2.54 m/s between par

Question

The water in a river flows uniformly at a constant speed of 2.54 m/s between parallel banks 85.9 m apart. You are to deliver a package directly across the river, but you can swim only at 1.46 m/s.

(a) If you choose to minimize the time you spend in the water, in what direction should you head?
____ ° from the direction of the stream
(b) How far downstream will you be carried?
____ m
(c) If you choose to minimize the distance downstream that the river carries you, in what direction should you head?
____ ° from the direction of the stream
(d) How far downstream will you be carried?
____ m

Explanation / Answer

given,

speed of stream = 2.54 m/s

distance = 85.9 m

speed of swimmer = 1.46 m/s

to minimize the time swimmer should head 90 degree from the direction of stream

time swimmer will take to cross the river = 85.9 / 1.46

time swimmer will take to cross the river = 58.835 sec

horizontal distance covered in this time = 58.835 * 2.54

distance downstream will be carried = 149.4409 m from the opposite side of the bank

to minimize the distance swimmer should head = 180 - tan^-1(1.46 / 2.54)

to minimize the distance swimmer should head = 150.11 degree from the direction of the stream

distance downstream will be carried = 0 m from the opposite side of the bank

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