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Question Number 153628 by otchereabdullai@gmail.com last updated on 08/Sep/21
A ball is thrown vertically upwards.  Its hight(h)meters at time( t)seconds  is given by h= 5+30t−5t^2 . Find the  maximum hight reached by the ball.
$$\mathrm{A}\:\mathrm{ball}\:\mathrm{is}\:\mathrm{thrown}\:\mathrm{vertically}\:\mathrm{upwards}. \\ $$$$\mathrm{Its}\:\mathrm{hight}\left(\mathrm{h}\right)\mathrm{meters}\:\mathrm{at}\:\mathrm{time}\left(\:\mathrm{t}\right)\mathrm{seconds} \\ $$$$\mathrm{is}\:\mathrm{given}\:\mathrm{by}\:\mathrm{h}=\:\mathrm{5}+\mathrm{30t}−\mathrm{5t}^{\mathrm{2}} .\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{maximum}\:\mathrm{hight}\:\mathrm{reached}\:\mathrm{by}\:\mathrm{the}\:\mathrm{ball}. \\ $$
Answered by mr W last updated on 08/Sep/21
h=5+30t−5t^2   h=50−5(t−3)^2 ≤50  h_(max) =50m at t=3s.
$${h}=\mathrm{5}+\mathrm{30}{t}−\mathrm{5}{t}^{\mathrm{2}} \\ $$$${h}=\mathrm{50}−\mathrm{5}\left({t}−\mathrm{3}\right)^{\mathrm{2}} \leqslant\mathrm{50} \\ $$$${h}_{{max}} =\mathrm{50}{m}\:{at}\:{t}=\mathrm{3}{s}. \\ $$

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