Answer:
she will fall to an height of 21.09° only, beyond such an height ; the spring will break.
Katya will not be able to swing to the platform because the angle will be between -21.09° and 21.09° from vertical
Explanation:
If the distance is from the point of angle A to angle B , partitioned by a perpendicular line in the middle then, The conservation of energy between A and B can be expressed as :
[tex]KE_A +PE_B = KE_B + PE_B[/tex]
[tex]0 + mgh = \frac{1}{2}mv_B^2+ 0[/tex]
where ; the height h = [tex]l ( cos \theta - \frac{1}{2})[/tex]
[tex]mgl ( cos \theta - \frac{1}{2}) = \frac{1}{2}mv^2_B[/tex]
[tex]\frac{mv_B^2}{l} = mg (2 cos \theta -1 )[/tex]
[tex]T = \frac{mv_B^2}{l}+ mg cos \theta[/tex]
T = mg(3 cos θ - 1)
Given that:
T = 180 % = 1.8 mg
Then:
1.8 mg = mg(3 cos θ - 1)
2.8 mg = (3 cos θ - 1)
cos θ = [tex]\frac{2.8}{3}[/tex]
θ = cos ⁻¹ (0.933)
θ = 21.09°
Therefore, she will fall to an height of 21.09° only, beyond such an height ; the spring will break.
Katya will not be able to swing to the platform because the angle will be between -21.09° and 21.09° from vertical
