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Sammy Sosa Leaf
June 8th, 2011 | 
Author: Sammy Sosa Leaf Currently For Sale On eBay
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Sammy Sosa Leaf
to all math people, easy ten points?
I'm really confused as to how to even solve this. Any help would be greatly appreciated!
sammy sosa throws the baseball with an initial speed of 145 feet per second at a 200 degree angle to the horizontal. The ball leaves Sammy's hand at 5 feet high. How long is the ball in the air?
This should be in physics. But that's not the real problem. I suspect you've left out some decimals here and that makes math types real uneasy. Sometimes even a bit cranky.
If it is 200 degrees, he's throwing it into the ground. So I assume it's 20.0.
The trick to realize here is that the vertical speed is the only thing that matters. The vertical speed allows gravity to work its powers and pull the ball down.
Step One
=======
To answer your question, we need only determine what the vertical speed is and work it as an ordinary problem.
If the angle is 20 degrees then the vertical speed is Vv = 145 ft/s*Sin(20)
Vv = the vertical speed = 49.59 ft/s
Step Two
======
Here's the physics part of it. We have to find the distance it goes up before it stops and the time for it to go up before it stops. Let's start with the distance. Up is the plus direction. Down is minus. I choose that just because, but they must be opposite.
d=?
a = - 32 ft/s
Vf = 0
Vf = the final speed. It is going to stop so it's zero.
Vi = 49.59 ft/s
Formula
Vf^2 = Vi^2 + 2ad
0 = 49.59 ^2 -2*32d
d = -2459/-64 = 38.429 feet
Step Two
=======
How long does it take to get up there?
d = 38.429 feet
Vi = 49.59 ft/sec
Vf = 0
t = ??
Formula
d = (vf + vi)*t/2
38.429 = (49.59+ 0) * t/2 Multiply both sides by t
76.858 = 49.59*t
t = 1.499 seconds.
Step three
=======
Here's where you start to work. This distance down increases by 5 feet. (Why?). The starting speed is zero this time. You don't know the ending speed because of the extra 5 feet so sadly you can't just repeat step two.
Finally you are looking for time.
d = vi*t + 1/2 a*t^2
d = 38.429 + 5 feet The distance is now minus because we are going down.
vi = 0
a = - 32 feet/sec^2 minus because it is acting downward
t = ???
I'll let you solve it. t = 1.64 about
You do not need a quadratic.
Phew!!! Lots of typing.
Step Four
=======
Add your times. Comes to a bit over 3 seconds.
NOTE: Are you in physics? If you are then the quick way to do this
d = -5 ft
vi = 49.5 ft/sec
a = - 32 ft/sec^2
Formula
d = vi*t + 1/2 a t^2
When you do this, you have to use the quadratic formula. Use t as your unknown thus
t = [-b +- sqr(b^2 - 4ac)]
a = 16
b = -49.5
c = -5
t comes to about 3.19
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