A man can still swim in water at speed 3km/h. He want to cross a river that flows at 2km/h and reach directly opposite to the starting point
1) find in which direction should he try to swim and find the angle of his body makes river fkowst
2) how much time will be take to cross the river if river is 500 width
draw a diagram
If he swims upstream at an angle of θ such that sinθ = 2/3
then his actual travel will be straight across the river.
The distance he actually swims is given by the hypotenuse of the triangle.
time = distance/speed
To solve this problem, we can use vector addition and trigonometry.
1) To find in which direction the man should try to swim, we need to calculate the angle at which his body should be positioned to counteract the river flow. Let's assume the river is flowing from east to west, and the man wants to reach a point directly opposite his starting point.
Since the river is flowing at a speed of 2 km/h, we'll represent its velocity as a vector (2, 0) in km/h (eastward direction). The man can swim at a speed of 3 km/h, so his velocity will be represented as a vector (3cosθ, 3sinθ), where θ is the angle the man makes with the eastward direction.
For the man to reach directly opposite the starting point, his body should be aligned with the river's current. This means the angle he makes with the eastward direction should be the same as the angle between the river's flow and the eastward direction. This angle will be:
θ = arctan(0/2) = 0° or 180°
Therefore, the man should try to swim either directly to the east or directly to the west.
2) To calculate the time taken to cross the river, we need to find the distance the man needs to swim. We are given that the river's width is 500 meters.
Since the man is swimming directly across the river, the distance he needs to travel can be found using the Pythagorean theorem:
Distance = √(width^2 + height^2)
= √(500^2 + 0^2)
= 500 meters
Using the man's swimming speed of 3 km/h, we can calculate the time taken:
Time = Distance / Speed
= 500 meters / 3000 meters/hour
= 1/6 hour
= 10 minutes
Therefore, it will take the man 10 minutes to cross the river.