Samantha threw and apple out of the window fr the tenth floor of her apartment building. the equation y= -16t^2 +120 can be used to represent the fruits height above the ground, where t represents time, in seconds, after she threw the apple. how long did it take the apple to hit the ground? round to the nearest hundredth.

Answer is 2.74  seconds



y= -16t²   +120 is a parabola with its vertex at (0, 120). it opens downwards.
since this parabola models the height above the ground, we need the time at which the height is equal to zero. this occurs at y = 0. set y = 0 and solve for t
      y = -16t² + 120
        0 = -16t² + 120
-120 = -16t²
15/2 = t²
      t² = 15/2
      t  =  ±√(15 / 2)

drop the negative solution because time isn't negative in this situation. the question says t is the number of seconds after the apple is thrown.

using calculator, we have

      t = 2.7386127 seconds

which rounds to the nearest hundredth as 2.74 seconds.
answer is 2.74  seconds

attached is the graph of  y= -16t²  +120, graphed in desmos