SOLUTION: One of the games at a carnival involves trying to ring a bell with a ball by hitting a lever that propels the ball into the air. If the ball is launched with an initial velocity of

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Question 839493: One of the games at a carnival involves trying to ring a bell with a ball by hitting a lever that propels the ball into the air. If the ball is launched with an initial velocity of 39ft/s, and the bell is 25 ft. above the ground, will it be hit by the ball?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The problem is assuming that there is no friction on the way up.
Probably not true, but anyway:
Let +h%28t%29+ = the height above ground the ball reaches
The equation is:
+h%28t%29+=+-16t%5E2+%2B+39t+
The +-16t%5E2+ is due to the force of gravity pulling down
------------------
I have to find the peak, or vertex
+t%5Bv%5D+=+-39%2F%282%2A%28-16%29%29+
+t%5Bv%5D+=+39%2F32+
Now I need to find +h%28+39%2F32+%29+
+h%28+39%2F3+2%29+=+-16%2A%28+39%2F32+%29%5E2+%2B+39%2A%28+39%2F32+%29+
+h%28+39%2F32+%29+=+-16%2A%28+39%2F32+%29%5E2+%2B+39%2A%28+39%2F32+%29+
+h%28+39%2F32+%29+=+-23.766+%2B+47.531+
+h%28+39%2F32+%29+=+23.765+
This is short of 25 ft, so the ball doesn't hit the bell
Here's the plot:
+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+30%2C+-16x%5E2+%2B+39x+%29+