The function given by f (t)= (-16t-8)(t-1) represents the height of a stone seconds after it was thrown by Clare. In both functions, height is measured in feet. *Whose stone hits the ground first?

Question

The function given by f (t)= (-16t-8)(t-1) represents the height of a stone seconds after it was thrown by Clare. In both functions, height is measured in feet. *Whose stone hit the water first? *When did that happen?

Answer 1

f(x) = (-16t -8)(t-1) = -16t^2 + 8t + 8

it hits the ground when f(x) =0

-16t^2 + 8t + 8 = 0

divide by -8

2t^2 -t -1 = 0

use the quadratic formula to solve for t

ignore the negative square root

t = 1/4 + (1/4)sqr(1 + 8) = 1/4 +3/4 = 1 second to hit the ground

it reaches a maximum height when -32t +8 = 0 or t = 1/4 second

max height = -16(1/16) + 8(1/4) + 8 = 9 feet, then in 3/4 second later it hits the ground