a man can swim in still water At 5 km/h . in order to cross the river through shortest path , at what approximate angle he should swim at, with the upstrem ?
Incomplete.
To determine the approximate angle at which the man should swim with the upstream to cross the river via the shortest path, we can use some basic trigonometry.
Let's assume that the speed of the river's current is V km/h and the man's speed in still water is 5 km/h. When he is swimming with the upstream, his effective speed will be reduced by the speed of the current. So his speed becomes (5 - V) km/h.
To cross the river in the shortest path, the man should swim directly perpendicular to the river's flow. This means his direction should be at a 90-degree angle to the river's current.
Now, we can use the concept of vector addition to find the resultant velocity of the man's swimming speed and the river current. The magnitude of the resultant velocity will give us the effective speed at the 90-degree angle.
Using the Pythagorean theorem, we can find the magnitude of the resultant velocity as follows:
Resultant Velocity = √((5 - V)^2 + V^2)
To find the approximate angle, we can use the trigonometric function of sine:
sin(θ) = Opposite / Hypotenuse
In this case, the opposite side is V and the hypotenuse is the resultant velocity. So the approximate angle (θ) the man should swim at with the upstream can be found by:
θ = sin^(-1)(V / √((5 - V)^2 + V^2))
Once you plug in the value of the river's current (V), you can calculate the approximate angle (θ) using a scientific calculator or any tool that can perform trigonometric calculations.