Katya is training for an upcoming gymnastics competition and needs to improve her upper body strength. At the moment, she can only support at most 180% of her body weight when she’s hanging off of equipment. Misha, a close friend and circus performer, suggests that she train on a swinging trapeze. Katya grabs onto the trapeze which hangs off a pair of cables of length ` that initially make an angle of 60.0◦ with the vertical. She steps off the platform and swings forward. To what height will she fall/rise as she swings? Will Katya swing back to the platform?

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 :

where ; the height h =

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 =

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

b) 10 minutes

girls stopped for 10 minutes.

the skeletons of most mammals reach a certain size and then stop growing. however, many animals, including some mammals, keep growing throughout their lives. kangaroos, for example, just keep growing and growing until they die. also, the longer an animal lives the greater the chance it might catch some deadly disease.