Q4 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 when the ball will hit the ground, we need to find when the height h is equal to 0. So we can set h = 0 in the function:
0 = -16t^2 + 30t + 6
This is a quadratic equation that can be solved by factoring, the quadratic formula, or completing the square. Factoring may not work in this case, so we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / 2a
For our equation:
a = -16, b = 30, c = 6
t = (-30 ± √(30^2 - 4(-16)(6))) / 2(-16)
t = (-30 ± √(900 + 384)) / -32
t = (-30 ± √1284) / -32
t = (-30 ± 35.81) / -32
Now we have two possible solutions, but we only consider the positive one as time cannot be negative in this context:
t = (-30 + 35.81) / -32
t = 5.81 / -32
t ≈ -0.18
Therefore, the ball will hit the ground after approximately 5.81 seconds.