Solving Pendulum Problem: Find h & Resultant Angle

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To solve the pendulum problem, the height (h) that the pendulum rises is calculated to be approximately 0.051 meters using the equation 1/2mv² = mgh. The next step involves determining the resultant angle using trigonometric relationships. A suggestion was made to draw a diagram and apply trigonometric functions, leading to the equation h = 7 tan(θ). The challenge remains in finding the actual angle θ from this relationship. The discussion emphasizes the importance of visualizing the problem to facilitate solving for the angle.
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Homework Statement



a 2 kg pendulum of length 7 meters is moving at 1 m/s, calculate how high (h) the pendulum will rise; and the resultant angle.


Homework Equations


1/2mv2 = mgh

cos = Y/L

h = L ( 1- cos )


The Attempt at a Solution



1/2(2)(1)^2 = (2)(9.8) h
1 = 19.6h
1/19.6h
h = .051

just don't know how to go about gettign resultant angle
 
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Have you tried drawing a diagram and writing out a trigonometric relationship using that diagram?
 
yeah i did and got h= 7 tan\theta, how would you find the actual angle that what I am having difficult with.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...

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