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Ronald is a baseball player.  When he hits a baseball, the height of the ball can be modeled by the following function, where t is the number of seconds after the ball is hit and h(t) is the height of the ball in feet after t seconds.

h(t)=−16t2+90t+4

a)  What is the maximum height that the ball reaches?

b)  How long does it take for the ball to reach its maximum height?

c) How long does it take for the ball to hit the ground?

Round all answers to the nearest tenth of a foot or second.

 Jun 15, 2020
 #1
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Ronald is a baseball player.  When he hits a baseball, the height of the ball can be modeled by the following function, where t is the number of seconds after the ball is hit and h(t) is the height of the ball in feet after t seconds.

h(t)=−16t2+90t+4

a)  What is the maximum height that the ball reaches?

b)  How long does it take for the ball to reach its maximum height?

c) How long does it take for the ball to hit the ground?

Round all answers to the nearest tenth of a foot or second.

 

Ronald ist ein Baseballspieler. Wenn er einen Baseball schlägt, kann die Höhe des Balls durch die folgende Funktion modelliert werden, wobei t die Anzahl der Sekunden nach dem Schlagen des Balls und h (t) die Höhe des Balls in Fuß nach t Sekunden ist.
a) Was ist die maximale Höhe, die der Ball erreicht?
b) Wie lange dauert es, bis der Ball seine maximale Höhe erreicht hat?
c) Wie lange dauert es, bis der Ball den Boden berührt?

 

Hello Guest!

 

\(h (t) = - 16t^2 + 90t + 4\)

 

b)

\(h'(t)=-32t+90=0\\ t=2.8125\)

\(2.8\ second\ does\ it\ take\ for\ the\ ball\ to\ reach\ ist\ maximum\ height.\)

 

a)

\(h (t) = - 16t^2 + 90t + 4\\ h (t) = - 16\cdot (2.8125)^2 + 90(2.8125) + 4\\ h(t)=130.5625\\ \color{blue}130.6\ foot\ is\ the\ maximum\ height\ that\ the\ ball\ reaches.\)

 

c)

\(h (t) = - 16t^2 + 90t + 4=0\)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\\ x = {-90 \pm \sqrt{90^2-4\cdot (-16)\cdot 4} \over 2\cdot (-16)}\\ x=\frac{-90\pm \sqrt{8356}}{-32}\\ x=5.669\)

\(5.7 \ second\ long\ does\ it\ take\ for\ the\ ball\ to\ hit\ the\ ground.\)

laugh  !

 Jun 16, 2020
edited by asinus  Jun 16, 2020

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