Question

Question #288b9

Answer 1

4 seconds.

Explanation:

Damn, this kid has got some seriously strong legs.

graph{-16x^2+64x [-72.2, 75.9, -4, 70]}

Comment aside, I think we should rewrite the function to best suit the current circumstance:
`f(t)=-16t^2+64t` where `t` is the time in seconds.
Now, we have a function of time. This graph above shows the relationship between the ball's height `f(t)` and the time that has passed `t`. In this case, when `f(t)=0` the ball is on the ground, as the height `f(t)` is zero.

Alright, so all we need to do is to find the difference in time. The difference in time, let's call it `Deltat` is the distance between the two x-intercepts (really t-intercepts should be more accurate, see graph).
`Deltat=t_2-t_1`

And the x-intercepts can be found using the quadratic formula:
`t=(-b+-sqrt(b^2-4ac))/(2a)`

With `a=-16,b=64,c=0`
`t=0 or 4`
`Deltat=4`

`:.` The time it takes for the ball to hit the ground is 4 seconds.