The height of a projectile launched upward at a speed of 32 feet/second from a height of 128 feet is given by the function h(t)=-16t^2+32t+128. How long will it take the projectile to hit the ground?
To find the time it will take for the projectile to hit the ground, we need to find the value of t when h(t) = 0.
Setting h(t) to 0:
-16t^2 + 32t + 128 = 0
Dividing through by -16 to simplify the equation:
t^2 - 2t - 8 = 0
Factoring the equation:
(t - 4)(t + 2) = 0
Setting each factor equal to zero and solving for t:
t - 4 = 0 or t + 2 = 0
t = 4 or t = -2
Since time cannot be negative, we can conclude that it will take 4 seconds for the projectile to hit the ground.