I am including part 1 for you to get the full description, but I need only part

Question

I am including part 1 for you to get the full description, but I need only part 2 number 14 answered. Please explain why and how thanks. Remember part 2 only. Thanks.

Walking by a pond, you find a rope attached to a stout tree limb 5.2 m off the ground. You decide to use the rope to swing out over the pond. The rope is a bit frayed but supports your weight. You estimate that the rope might break if the tension is 56 N greater than your weight. Your mass is 36 kg. You grab the rope at a point 4.2 m from the limb and swing out over the pond. The acceleration of gravity is 908 m.s2. In the figure, your initial position is designated with the numeral 1, the point at which you release the roped and begin to fall with a 2, and your point of impact with the water is identified with a 3. What is the maximum safe initial angle theta between the rope and the vertical at which it will not break during the swing? Answer in units of 22.98 degree Hint: Consider yourself as point of particle, as indicated in the figure. If you begin at this maximum angle, and the surface of the pond is 1.4 m below the level of the ground, with what speed will you enter the water if you let go of the rope when the rope is vertical? Answer in units of m/s

Explanation / Answer

applying work energy theorem we get

Wg = KE

sp mgh= 1/2*m*v^2

so

h=(5.2+1.4- 4.2 cos22.98)

h= 2.7333 m

so v= sqrt(2gh)

V= sqrt(2*9.8*2.7333)

v= 7.32 m/s

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