Juan hits a baseball. The equation #h=-16t^2+120t# models the height h, in feet, of the ball after t seconds. How long is the ball in the air?

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Answer 1 · 2017-07-15T10:30:24

When the ball returns to ground level, #h=0#, so:

#-16t^2+120t=0#

This is a quadratic equation we can solve to find the roots #t=0# or #t=7.5# #s#, which correspond to the beginning and end of the ball's flight.

For a quadratic in the form #ax^2+bx+c=0#

We know:

#t=(-b+-sqrt(b^2-4ac))/2a#

For

#-16t^2+120t=0#

#a=-16, b=120, c=0#

So:

#t=(-120+-sqrt(120^2-0))/-32=(-120+-120)/32=0/-32 or -240/-32#

Therefore:

#t=0# or #t=7.5# #s#