You throw a ball upward. Its height h, in feet, after t seconds can be modeled by the function h = -16t^2 + 30t + 6 After how many seconds will it hit the ground?
To find the time it takes for the ball to hit the ground, we need to find when the height h equals 0.
So, we set the function h = -16t^2 + 30t + 6 equal to 0:
-16t^2 + 30t + 6 = 0
Now, we need to solve this quadratic equation. We can either use the quadratic formula or factor the equation. In this case, factoring is simpler:
-16t^2 + 30t + 6 = 0
-2(8t^2 - 15t - 3) = 0
-2(8t + 1)(t - 3) = 0
Setting each factor to zero gives us two possible values for t:
8t + 1 = 0 or t - 3 = 0
8t = -1 or t = 3/1
t = -1/8 or t = 3
Since time cannot be negative, we disregard the negative solution. Therefore, the ball will hit the ground after 3 seconds.