Freefall Question: Proving Greater Speed Increase

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The discussion revolves around a physics problem involving two balls dropped from a height of 32.5 meters, one dropped freely and the other thrown downwards at 11 m/s. Initial calculations indicated the first ball takes 2.57 seconds to reach the ground, while the second takes 1.68 seconds. The confusion arose regarding whether the increase in speed referred to acceleration or the difference between initial and final velocities. Ultimately, it was clarified that the calculations were initially incorrect due to a misunderstanding of units, specifically mistaking velocity for acceleration. The correct interpretation reveals that both balls experience the same acceleration due to gravity, but their final velocities differ based on their initial speeds.
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The question is basically:
You are on top of a edge that is 32.5m high and you drop 1 ball, moments later you throw a 2nd ball at the initial speed of 11 m/s. Which ball has a greater increase in speed, or is the increase the same? and prove it with a calculation.

I started out with the x=x0 + v0t = .5at^2

For the first ball I got the time to be 2.57 s and for the second ball i got the time to be 1.68 s.
i proceed to try and work it out finding the velocity by using the v = v0 + at. and got -25.21 m/s^2 for the first ball and -27.53 m/s^2 for the 2nd.

this is where i have the problem. is the increase in the speed talking about acceleration? because if it is acceleration then shouldn't both ball have the same increase in speed because gravity is working on both of them equally?
 
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It sounds to me like there asking which ball has the biggest difference between there initial v and there final v.
 
ahh i see. then for the first ball the change in v is 25.21 m/s^2 because the initial v was 0. But then for the 2nd ball the Vf is 27.53 m/s^2 but does the mean the Vi is 11 m/s? cause if i remeber correctly, units must be the same to be added or subtracted. or am i missing something?
 
Sounds to me like they're asking how the hypotenuse of a triangle compares to the total length of its other sides.
 
Why does your Velocity have m/s^2 as units? m/s^2 is acceleration!
 
i can't believe it. i wrote down gravity as 9.81 m/s not 9.81 m/s^2. sigh. everything works out fine now.
thanks EP.
 
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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