h=-16t^2+16t+320

Answer 1

h represents the height of an object after t seconds

16 = the initial velocity

320 = the initial height in feet

-16t^2 represents the deceleration due to gravity

maximum height is found by taking the derivative

-32t +16 = 0

t = 16/32 = 1/2 second

h(1/2) = -16(1/2)^2 + 16(1/2) + 320 = 324 feet = maximum height reached in half a second

It hits the ground when h=0

h(t) = 0 = -16t^2 +16t + 320

16t^2 -16t -320 = 0

t^2 -t -20 = 0

(t-5)(t+4) = 0

t = 5 seconds to reach the ground

those are the usual problems associated with that quadratic equation

you know it's in feet, not meters, since if it were in meters the quadratic term would be -4.9t^2

gravity on earth at sea level has deceleration of 32 feet per second per second or

9.8 meters per second per second, approximately, but a very close approximation