What Was the Initial Speed of a Ball Thrown Horizontally from a Building?

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A ball thrown horizontally from a 58 m tall building lands 50 m away, prompting a discussion on calculating its initial speed. The vertical motion is analyzed using the equation for free fall, leading to a time of approximately 5.918 seconds. Initially, the user mistakenly included vertical velocity in their calculations, but later recognized that the initial vertical speed is zero. After correcting their approach, they determined that the initial horizontal speed is 14.57 m/s. This problem illustrates key principles of projectile motion and the independence of horizontal and vertical components.
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Hey, everyone! Glad I found this forum, I plan to be using it a lot to try to expand my Knowledge, I currently taking an AP Physics class in my high school with no prior physics experience. The teacher however is really great! Anyway let's see what we got going here.
(Note ▲=Delta)

Homework Statement



A ball is thrown horizontally from the roof of a building 58 m tall and lands 50 m from the base. What was the ball's initial speed?

Vertical Known
▲Y=-58
A Sub Y = -9.8m/s
t=5.918s
VnotY=?

Horizontal Known
▲X=50m
VnotX= ?

Homework Equations


t=5.918
I got this because assuming that the distance of 58m was traveled going a speed of -9.8m/s (g) it equals 5.918! (Hopefully)

The Attempt at a Solution


Its a long shot but I attempted to compare it to a problem done in school which was essentially the same but, involved an angle of the stone coming off the roof. Also different Knows were given. So this was my go&delta Y=(VnotX)(t)² + (.5)(g)(t)² I put in what I know

-58=(VnotY)(5.91)² + (4.9)(5.91)² Attempted to solve for VnotY

-58=(VnotY)(34.9281) + (171.14)

(VnotY)=(34.9281)+(229.14) I added the -58 over

(VnotY)=264.07 : ( I don't think this is right...

So that is where I am, I may be completely off...

Ok! So I looked at the problem again found an Inherent flaw,

▲y=(VnotY)(t)+(.5)(g)(t)²

SO! It turns out (VnotY) is Zero...Making that all Null and void...
So with some Algebra Magic I get t=3.43! With this I hope to get further...Will keep posted!

Another Update!
While looking through my book found that while somthing is in free fall it has 0 Acceleration in the X-Axis! So that voids Half of the Equation! Woo Go Physics! Making it simple and I found that the initial speed was 14.57
 
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well done!
 
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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