Tetherball is a game played by kids. The equipment consists of a volleyball on a string, with the other end of the string tied to the top of a post. Kids hit the ball back and forth around the post. Consider a volleyball of total mass 200 g attached to the top of a post by a 2 m long cord. The volleyball is traveling in a horizontal circle with a speed of 2 m/s. What is the angle θ between the post and the cord in degrees?

Details and assumptions
The acceleration of gravity is −9.8 m/s2.
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Tsinθ = mv²/R

Tcosθ = mg
tanθ=v²/Rg

dont get it

Please can you tell the numerical value

To find the angle θ between the post and the cord, we can use the concept of centripetal force.

Centripetal force is the force that keeps an object moving in a circular path. In this case, the tension in the cord is providing the centripetal force to keep the volleyball moving in a horizontal circle.

The centripetal force can be expressed as the product of the mass of the volleyball (m), the speed of the volleyball (v), and the radius of the circle (r).

F = m * v^2 / r

In this problem, we are given the mass of the volleyball as 200 g (or 0.2 kg), the speed of the volleyball as 2 m/s, and the length of the cord as 2 m. We also know the acceleration due to gravity is -9.8 m/s^2.

Let's assume that the angle θ is the angle between the cord and the vertical direction. The vertical component of the tension in the cord will balance the weight of the volleyball:

F_vertical = m * g = -0.2 kg * (-9.8 m/s^2) = 1.96 N

The horizontal component of the tension in the cord provides the centripetal force:

F_horizontal = F = m * v^2 / r

Since F_horizontal is perpendicular to the vertical component, we can use trigonometry to find the relationship between these two forces:

F_horizontal = F * cos(θ)

Now we can solve for the angle θ:

θ = arccos(F_horizontal / F) = arccos(m * v^2 / (r * F))

θ = arccos((0.2 kg * (2 m/s)^2) / (2 m * 1.96 N))

Calculating this expression will give you the value of θ in radians. To convert it to degrees, multiply by 180/π.

θ = θ_in_radians * (180/π)