The water in a river flows uniformly at a constant speed of 2.27 m/s between parallel banks 69.3 m apart. You are to deliver a p
ackage directly across the river, but you can swim only at 1.58 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?
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To solve this problem it is necessary to apply the concepts related to gravity as an expression of a celestial body, as well as the use of concepts such as centripetal acceleration, angular velocity and period.
PART A) The expression to find the acceleration of the earth due to the gravity of another celestial body as the Moon is given by the equation
Where,
G = Gravitational Universal Constant
d = Distance
M = Mass
Radius earth center of mass
PART B) Using the same expression previously defined we can find the acceleration of the moon on the earth like this,
PART C) Centripetal acceleration can be found throughout the period and angular velocity, that is
At the same time we have that centripetal acceleration is given as
Replacing