A river is flowing with a speed of 8 km/h.a swimmer wants to reach point R from P.he swims with a speed of 8km per h.at an angle of theta greater than 90degree w.r.t river flow.if PQ=QR=800mthen value of thea is????????!option are,90°,.60°,45°,30°
I think you need to clear this up.
Where are Q and R in relation to P?
You have said that θ > 90°, yet none of the choices is greater than 90°. Eh?
However, you appear to have an isosceles right triangle ...
To find the value of theta (θ), we need to use the concept of vector addition.
Let's consider the swimmer's velocity as a vector Vswim, which has a magnitude of 8 km/h and an angle of θ (greater than 90 degrees) with respect to the river flow.
The river's velocity is given as 8 km/h in the direction from point P to point Q. We can represent this velocity as a vector Vriver.
To find Vriver, we need to break it down into its horizontal and vertical components. Since the swimmer's velocity is parallel to the river's velocity, we can infer that the horizontal component of Vriver is equal to the swimmer's velocity, which is 8 km/h. The vertical component of Vriver is 0 km/h since the river is not flowing vertically.
Now, we can add the vector Vriver to the vector Vswim to find the resultant velocity vector Vresultant.
The magnitude of the resultant velocity vector Vresultant can be calculated using the Pythagorean theorem:
Vresultant = sqrt((Vswim + Vriver)^2)
Given that PQ = QR = 800m, we can consider PQ as the horizontal component of the displacement vector and QR as the vertical component of the displacement vector.
Using trigonometry, we can write:
PQ = Vresultant * cos(θ)
QR = Vresultant * sin(θ)
Substituting the given values, we have:
800m = sqrt((8km/h + 8km/h * cos(θ))^2) * cos(θ)
800m = sqrt((16km/h * (1 + cos(θ)))^2) * cos(θ)
800m = 16km/h * (1 + cos(θ)) * cos(θ)
800m = 16km/h * cos(θ) + 16km/h * cos^2(θ)
Let's solve this equation to find the value of θ.
800m - 16km/h * cos(θ) = 16km/h * cos^2(θ)
800m/16km/h - cos(θ) = cos^2(θ)
50s - cos(θ) = cos^2(θ)
Now, using trial and error or solving through methods like graphical, numerical, or algebraic methods, we can find the value of θ.
Unfortunately, without the actual numerical values provided for θ, it is not possible to determine the exact value of θ. Therefore, none of the given options (90°, 60°, 45°, 30°) can be confirmed as the correct answer without the specific numerical value of θ.