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A ball is thrown from an initial height of 3 meters with an initial upward velocity of 20m/s. The ball's height (in meters) after seconds is given by the following h=3+20t-5t^2. Find all values of t for which the ball's height is 13 meters.

 Jun 15, 2022
 #1
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-5t^2 + 20t + 3 =  13              subtract 13 from  both sides

 

-5t^2  + 20t  - 10  =  0            divide through by -5

 

t^2  - 4t + 2  =  0                   

 

Using the quadratic formula

 

 

t =   4 ±   sqrt [ 4^2 - 4 (1) (2) ]                4 ±  sqrt [ 8]       4 ± 2sqrt (2)

       _____________________  =        ___________  =  __________  =

                     2 * 1                                           2                     2

 

2 ± sqrt (2) =      about .59 sec   and   about 3.4 sec 

 

cool cool cool    

 Jun 15, 2022

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