Question

Where did I go wrong? Stop me when I go through the steps I took if you see my error plz!!!!

The height h in feet of a baseball hit from home plate can be modeled by the function h(t) = -16t^2 + 32t + 5.5, where t is the time in seconds since the ball was hit. The ball is descending when it passes 7.5 feet over the head of a 6-foot player standing on the ground. To the nearest tenth of a second, how long after the ball is hit does it pass over the player's head? (Enter only the number rounded to the nearest tenth.)

Answer 1

-16t^2+32t+5.5=7.5

Answer 2

I actually think I see it, is it supposed to =13.5 ft instead because it is 7.5 feet over a 6 ft players head?

Answer 3

\[-16t^2+32t+5.5=13.5\]
\[-16^2+32t-8=0\]
\[x=\frac{ -32\pm \sqrt{32^2-4\times-16\times-8} }{ 2\times-16 }\]

Answer 4

\[x=\frac{ -32 \sqrt{1,024-512} }{ -32 }\]

Answer 5

\[x=\frac{ -32\pm22.627416998 }{ -32 }\]

Answer 6

\[x=\frac{ -32+22.627416998 }{ -32 } = 0.29289322\]
\[x=\frac{ -32-22.627416998 }{ -32 } = 1.70710678\]

Answer 7

looks good. be sure to round.

notice that in the original equation
\[ −16t^2+32t−8=0 \]
you could first simplify by dividing each term by 8 to get
\[ -2t^2 +4t -1=0 \]
you will get the same answer, but with smaller numbers, you have less of a chance of making an error.

Answer 8

The next question says "The horizontal distance between the player and home plate is 120 ft. Use your answer from the previous question to determine the horizontal speed of the ball to the nearest foot per second." I just divide 120 by 1.7 to get the answer right?

Answer 9

yes