Ball's Acceleration: How to Calculate with Initial and Final Time and Height

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The discussion focuses on calculating an object's acceleration using initial and final time and height. The equation s = ut + (1/2)at² is central to the calculations, with participants exploring the correct values for initial velocity (u) and height (h). Initial attempts led to confusion, particularly regarding the correct application of the equation and the relationship between height and position at different times. Ultimately, the correct approach involves using the average of initial and final velocities to relate height and time. The final consensus indicates that the correct answer to the problem is D.
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The question is attached.
The correct answer is D

I got it as C first using the equation s=ut+1/2 a t^2
I took s as h, and t= (t2-t1)

I put u=0, which I discovered isn't correct. I then tried putting u=at1 and got a complex equation and got stuck there.
 

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You need to understand that the equation

s = ut + (1/2)at2

gives the position of the object at any time t. In other words, you give me the time and I will use the equation to find the position of the object. So

1. At time t1 the object is at s1 = ut1 + (1/2)at12

2. At time t2 the object is at s2 = ut2 + (1/2)at22

What is u? How is h related to s1 and s2?
 
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I'm sorry, I still don't get it. How do you solve this question?
 
What part exactly of my previous posting don't you get?
 
I finally found it. I used this equation

s=h
u=at1
v=at2
t=(t2-t1)

\frac{s}{t}=\frac{u+v}{2}
 
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 .
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