Consider a swimmer who wants to swim directly across a river. If the speed of the current is 0.31 m/s and the swimmer's speed relative to the water is 0.57 m/s, how long will it take her to cross a river that is 13 m wide?
If
vave = (change of displacement)/(time elapsed)
then,
t = (change of displacement)/(average velocity)
SO,
t = (13 meters)/(0.57 m/s) = 22.8 s
To find out how long it will take the swimmer to cross the river, we need to analyze the motion of the swimmer in relation to both the current and the distance she needs to cross. Let's break it down step by step:
1. Determine the horizontal component of the swimmer's velocity:
The swimmer's velocity relative to the water is 0.57 m/s. This represents the horizontal component of her velocity. We will refer to this as Vswimmer.
2. Determine the velocity of the current:
The current's velocity is given as 0.31 m/s. This represents the velocity at which the river is flowing. We will refer to this as Vcurrent.
3. Calculate the resultant velocity:
The resultant velocity, Vresultant, is the vector sum of the swimmer's velocity relative to the water and the velocity of the current. It represents the actual velocity at which the swimmer will move across the river.
Vresultant = √(Vswimmer^2 + Vcurrent^2)
Vresultant = √(0.57^2 + 0.31^2) = √(0.3249 + 0.0961) = √0.421 = 0.65 m/s (rounded to two decimal places)
4. Calculate the time taken to cross the river:
The time taken can be determined using the formula: time = distance / velocity.
Given that the distance to be crossed is 13 m, and the resultant velocity is 0.65 m/s, we can calculate the time taken:
time = distance / velocity
time = 13 m / 0.65 m/s = 20 seconds
Therefore, it will take the swimmer 20 seconds to cross the 13 m wide river.