check the picture below. notice when it hits the ground, y = 0 that is, f(t) = 0.
Ball1 is is dropped from 126ft, thus f(t) = -16t² + 126, now, Ball2 is dropped from 271ft, f(t) = -16t² + 271.
[tex]\bf \textit{Ball1 hits the ground at}
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0=-16t^2+126\implies 16t^2=126\implies t^2=\cfrac{126}{16}\implies \boxed{t=\sqrt{\cfrac{126}{16}}}
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\textit{Ball2 hits the ground at}
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0=-16t^2+271\implies 16t^2=271\implies t^2=\cfrac{271}{16}\implies \boxed{t=\sqrt{\cfrac{271}{16}}}[/tex]
