Question

1. you are crossing a river that moves at a velocity of 2.45 m/s and the direct of flow is toward the west. (the top of this page is north). the river you are crossing is 450 meters wide and the boat you are using to cross will move with a velocity of 6.8 m/s. please calculate how far upstream you need to aim to land directly across the river. (point c). you will need to draw a picture of this with a starting point of a on the south shore, and points b & c on the north shore.

Explanation:

Step1: Find the time to cross the river

The velocity of the boat perpendicular to the river (assuming we aim upstream to cancel the river's drift) is \(v_{y}\). The width of the river \(d = 450\ m\). The velocity of the boat \(v_{boat}=6.8\ m/s\).
The time \(t\) to cross the river is given by \(t=\frac{d}{v_{boat}}\) (using the component of the boat's velocity perpendicular to the river flow for crossing).
\(t=\frac{450}{6.8}\ s\approx66.18\ s\)

Step2: Calculate the distance upstream

The velocity of the river \(v_{river} = 2.45\ m/s\). The distance \(x\) upstream (to cancel the river's drift) is given by \(x = v_{river}\times t\) (because the time taken to cross the river is the same as the time for which the river would have carried the boat downstream if not aimed upstream).
Substitute \(t=\frac{450}{6.8}\ s\) and \(v_{river}=2.45\ m/s\) into \(x = v_{river}\times t\)
\(x=2.45\times\frac{450}{6.8}\ m\)
\(x=\frac{2.45\times450}{6.8}\ m=\frac{1102.5}{6.8}\ m\approx162.13\ m\)

Answer:

The distance upstream you need to aim is approximately \(162\ m\)