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The equation $y = -16t^2 + 26t + 105$ describes the height (in feet) of a ball tossed up in the air at 26 feet per second from a height of 105 feet above the ground. In how many seconds will the ball hit the ground? Express your answer as a decimal rounded to the nearest tenth.

 Aug 28, 2022
 #1
avatar+33151 
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Set y = 0 and solve the resulting equation for t.  There will be two values; choose the only sensible one.

 Aug 28, 2022
 #2
avatar+29 
-3

I remember seeing this problem in Alcumus, or maybe a similar variation of it. However, the solution is pretty simple. 

set y = 0, since we are trying to find out when the ball hits the ground, and when that happens, Y = 0. 

This looks like a quadratic formula! 

\(0 = -16t^2 + 26t + 105\)

Then, simply solve for this quadratic. There will be two answers, but one of them is negative, so choose the postitve answer.

 

\(\frac{-26 +\sqrt{26^2 - 4(-16)(105)} }{2(-16)}\) 

That should be the postive answer. Sorry, it's a little messy. Solve this equation and the answer shall be the final answer!

 

Hope this helps!

 Aug 28, 2022

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