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The equation 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
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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
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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