A helicopter pilot drops a package when the helicopter is 200 ft. above the ground, rising at 20 ft/sec.

How long will it take for the package to hit the ground? What is the speed of the package at impact?

I know you set s(t) equal to zero, so -16(t^2)+20t+200=0, but factoring it out I get really obscure values for t. I'm wondering if there's another way to do it.

1 answer

-16t^2+20t+200=0
divide by -4
4t^2 - 5t - 50 = 0
This does not factor, so use the formula

t = (5 ± √825)/8
= 4.2 or a negative

but since t > 0

t = 4.2 seconds