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The height h metres of a ball at time t seconds after it is thrown up in the air is given by the expression: h = 1 + 15t - 5t^2
(i) find the times at which the height is 11m.
(ii) Use your calculator to find the time at which the ball hits the ground.
(iii) What is the greatest height the ball reaches?

 Jul 9, 2021
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(i)      -5t^2  +  15t  +  1   =  11

          -5t^2  +  15t  - 10   =  0       divide through by -5

            t^2   -  3t   +  2     =  0       factor

            (t  - 2)  ( t - 1)   =   0

             At 11m  at     1sec    and  2 sec

 

(ii)       -5t^2  + 15t  +  1   =  0

             5t^2   - 15t  -  1   =  0

            Hits  the  ground  at  ≈  3.06 sec     (from WolframAlpha)

 

(iii)     Greatest  height reached  at time    (-15) / (2 (-5) )   =   15/10  =  1.5 sec

 

Max  ht =    -5(1.5)^2  + 15 (1.5)   + 1   =   12.25  m

 

 

cool cool cool

 Jul 9, 2021

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