Lesson Physics as Gravity (Mathematical)

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This Lesson (Physics as Gravity (Mathematical)) was created by by Nate(3500) About Me : View Source, Show
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Notice: This is when you throw an object vertically.
Equation to notice: f%28t%29+=+-16t%5E2+%2B+vt+%2B+h where t is time .. v is initial velocity ..h is the height above the ground .. f%28t%29 is the height after t seconds
Example:
I toss a 5 pound ball vertically at an initial rate of 32 meters per second from the top of a water tower that is 10 meters tall.
v = 32
h = 10
f%28t%29+=+-16t%5E2+%2B+32t+%2B+10
When will the ball hit the ground?
0+=+-16t%5E2+%2B+32t+%2B+10
0+=+-8t%5E2+%2B+16t+%2B+5
t+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F%282a%29
t+=+%28-16+%2B-+sqrt%2816%5E2+-+4%28-8%29%285%29%29%29%2F%282%28-8%29%29
t+=+%28-16+%2B-+sqrt%28+256+%2B+160+%29%29%2F%28-16%29
t+=+%28-16+%2B-+sqrt%28416%29%29%2F%28-16%29
t+=+1+%2B-+sqrt%28416%29%2F%28-16%29
Look at the positive time:
t+=+1+-+sqrt%28416%29%2F%28-16%29
The ball would hit the ground after about 2.2748 seconds.
What is the maximum height the ball would reach, and when is that?
Vertex: ((-b/2a),f(x)) = (1,26)
After one second, the ball will reach its max height: 26 meters ....
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