Step 1: Look in your book or online for the conical pendulum equation.
Step 2: Look at the drawing and see which angle is involved in the equation.
Answer: It's Angle #2 in your drawing.
The answer to your question would be C
Answer:
500ms times 2 would be when the ball reaches the max horizontal distance.
Then to find the angle, use the formula of time to reach max height t = u sin theta / g . With t being the max height time 500ms, u being 10m/s
For initial vertical velocity just use u sin theta.
Answer:
Her angular speed (in rev/s) when her arms and one leg open outward is 
Explanation:
Initial moment of inertia when arms and legs in is 
Final moment of inertia when her arms and on leg open outward, 
Initial angular speed 
Let the final angular speed be 
Since external torque on her is zero so we can apply conservation of angular momentum

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Thus her angular speed (in rev/s) when her arms and one leg open outward is 