Final answer:
By solving the quadratic equation -16t^2 + 64t + 4 = 0, we find the time it takes for a baseball hit from 4 feet off the ground at an initial velocity of 64 feet per second to reach the ground.
Step-by-step explanation:
If a baseball player hits a baseball from 4 feet off the ground with an initial velocity of 64 feet per second, we can determine how long it will take for the baseball to hit the ground using the provided equation h = -16t2 + 64t + 4, where h represents the height in feet, and t is the time in seconds. We need to find the time t when the height h is 0, representing the moment the ball hits the ground.
To solve for t, we set the equation to zero, and solve for t:
0 = -16t2 + 64t + 4
We can simplify this equation by dividing all terms by -4, leading to:
0 = 4t2 - 16t - 1
Solving this quadratic equation by applying the quadratic formula:
t = [-(-16) ± √((-16)2 - 4(4)(-1))]/(2(4))
t = [16 ± √(256 + 16)]/8
t = [16 ± √(272)]/8
Since time cannot be negative in this context, we discard the negative root and simplify the positive root:
t = (16 + √272) / 8
Calculating this value to the nearest hundredth gives us the time it takes for the baseball to hit the ground.