Question

Samantha threw an apple out of a window. The equation -16t^(2)+120=y can be used to represent the apple's height above the ground, where t = time in seconds after she threw the apple. how long did it take for the apple to hit the ground. Round to nearest hundredth

Answer 1

Check the picture below, y = 0 when that happens

$\bf -16t^2+120=0\implies 120=16t^2\implies \cfrac{120}{16}=t^2\implies \cfrac{15}{2}=t^2 \\\\\\ \sqrt{\cfrac{15}{2}}=t$

bear in mind the square root would give us a +/- roots, however, since this is seconds, a negative unit would be unfeasible, thus we only used the positive root from it.