Remember that when the ball hits the ground, s(t) = 0
So we have: -16t^2 - 32t + 48 = 0
It's time to determine t = (-(-32) +/- sqrt((-32)^2 - 4(-16)(48))) / (2(-16))
t = (32 +/- sqrt(1024 + 3072)) / (-32)
t = (32 +/- sqrt(4096)) / (-32)
t = (32 +/- 64) / (-32)
t = (48 or -32) / (-32)
t = -1.5 or 1
Since a negative number doesn't make sense, so t =1
Keep in mind that velocity is the derivative of the height, therefore:
s'(t) = -32t - 32
s'(t) = -32*1 - 32
s'(t) = -32 - 32
s'(t) = -64
So the answer 64 feet per second dwn
