A man can swim in still water at a speed of 3km/hr.He wants to cross the river that flows at 2km/hr and reach the point directly opposite to his starting Point.find the angle if his body makes with the river flow.
41.8
3sin@=2
To find the angle that the man's body makes with the river flow, we can use trigonometry.
Let's assume that the man's body makes an angle θ with the river flow. We can also assume that the width of the river is d kilometers.
When the man swims across the river, his resultant velocity (velocity relative to the ground) will be the vector sum of his swimming velocity and the river's flow velocity.
The velocity of the man in the still water is 3 km/hr, and the velocity of the river's flow is 2 km/hr. Since these velocities are perpendicular to each other, we can use the Pythagorean theorem to find the resultant velocity.
Resultant velocity = √(3^2 + 2^2) = √13 km/hr
Now, using trigonometry, we can calculate the angle θ. The sine of the angle θ is equal to the opposite side (2 km/hr) divided by the hypotenuse (√13 km/hr).
sin(θ) = 2/√13
To find the angle θ, we can take the inverse sine (arcsine) of both sides:
θ = arcsin(2/√13)
Using a calculator, we find that θ is approximately 33.69 degrees.
Therefore, the angle that the man's body makes with the river flow is approximately 33.69 degrees.
Vsw = Vs + Vw = 3 + 2i, Q1.
Tan A = 2/3 = 0.66667.
A = 33.7o E. of N.
Body angle = 33.7o W. of N.