Question

A swimmer heads directly across a river, swimming at 1.00 m/s relative to still water. He arrives at a point 41.0 m downstream from the point directly across the river, which is 73.0 m wide. What is the speed of the river current?

Answer 1

The speed of the river current is calculated by dividing the downstream distance (41.0 m) by the time taken to cross the river (73.0 s), which gives approximately 0.56 m/s.

Step-by-step explanation:

To find the speed of the river current, we need to analyze the swimmer's motion across the river. Given that the swimmer swims at a speed of 1.00 m/s relative to still water and arrives 41.0 m downstream after crossing a river that is 73.0 m wide, we can use the Pythagorean theorem to model the swimmer's path as the resultant of two perpendicular vectors: the swimmer's velocity relative to the water, and the speed of the river current.

The time it takes for the swimmer to reach the other side can be found using the width of the river and the swimmer's speed:

Time = Width of River / Swimmer's Speed = 73.0 m / 1.00 m/s = 73.0 s.

Using the time, we can calculate the speed of the river current: River Current Speed = Downstream Distance / Time = 41.0 m / 73.0 s ≈ 0.56 m/s.

Therefore, the speed of the river current is approximately 0.56 m/s.

Answer 2

velocity of the river is equal to 0.56 m/s

Step-by-step explanation:

given,

velocity of swimmer w.r.t still water = 1 m/s

width of river = 73 m

he arrives to the point = 41 m

`times = (distance)/(speed)`

`times = (73)/(1)`

t = 73 s

`velocity = (distance)/(time)`

=
`(41)/(73)`

= 0.56 m/s

velocity of the river is equal to 0.56 m/s