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Hello, Please assist me with my homework assignment   A batter hits a fly ball. A...

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novjb | Salutatorian

Posted May 16, 2013 at 11:19 PM via web

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Hello,
Please assist me with my homework assignment
 
A batter hits a fly ball. A scout in the stands makes the following observations
Time       .75    1.5     2      2.75      3.25      4.75
 
height     77    133    160    187       194      169
 
 This is a quadratic function correct?
 
Use a graphing calculator to perform the regression for the best fit equation. Write the resulting equation below, rounding to the nearest hundredth.
 
I think it is –15.9x^2+110.48x+3.02        Is this right?
 
 
Determine the initial velocity of the baseball and the height of the ball when hit. Round to the nearest hundredth.
h=-15.9t^2+110.48t+3.02 h=-15.9(0)^2+110.48(0)+3.02=3.03  3.03 is this the height?
h=-15.9t^2+vt+s     110.48 =v 110.48 is the velocity?
 
Calculate how many seconds an the outfielder has to position himself for the catch if he intends to catch the ball 6 feet above the ground. Show your work and round to the nearest hundredth
 

How do I solve this?

1 Answer | Add Yours

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pramodpandey | College Teacher | Valedictorian

Posted May 17, 2013 at 4:08 AM (Answer #1)

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We have given

`h=-15.9t^2+110.48t+3.02`

`` At maximum height , its velocity should be zero.

So differenciate with respect to t

`(dh)/(dt)=-2xx15.9t+110.48`

`(dh)/(dt)=0`

`if`

`-31.8t+110.48=0`

`t=110.48/31.8`

`t=3.47 sec.`

`(d^2h)/(dt^2)=-31.8<0`

Thus at  t=3.47 sec , we have maximum height.

maximum height= -15.9 (3.47)^2+110.48(3.47)+3.02

=194.47 feet.

The distance ball will have to cover after attaining maximum height ,before it catched= (194.47-6)

=188.47 feet.

Substitute h=188.47 feet in given equation

h=-15.9t^2+110.48t+3.02

Thus we have

`188.47=-15.9t^2+110.48t+3.02`

`15.9t^2-110.48t+185.45=0`

solving the quadratic equation

`t=(110.48+-sqrt(110.48^2-4xx185.45xx15.9))/(2xx15.9)`

`t=(110.48+-20.28)/31.8`

`t=4.11 or 2.84`

To attained maximum height ball took 3.47 sec. so in returnjourney it should take less time tahn 3.47.

Thus  t=2.84 sec.

Thus outfielder has to position himself for the catch if he intends to catch the ball =2.84+3.47=6.30 sec.

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