After a baseball is hit, the height h (in feet) of the ball above the ground t seconds after it is hit can be approximated by the equation h=-16t^2+70t+4. Determine how long it will take for the ball to hit the ground. Round your answer to two decimal places.
When it hits the ground, h=0
solve for that time. It is a quadratic, use the quadratic equation.
To determine how long it will take for the ball to hit the ground, we need to find the value of t when the height (h) is equal to zero. We can do this by setting the equation equal to zero and solving for t.
The given equation is:
h = -16t^2 + 70t + 4
Setting h = 0, we have:
0 = -16t^2 + 70t + 4
Now, we need to solve this quadratic equation. We can either factor it, complete the square, or use the quadratic formula. In this case, factoring may not be possible, and so, we'll use the quadratic formula:
The quadratic formula is given by:
t = (-b ± √(b^2 - 4ac)) / (2a)
Here, a = -16, b = 70, and c = 4. Substituting these values into the quadratic formula, we get:
t = (-70 ± √(70^2 - 4(-16)(4))) / (2(-16))
Simplifying further:
t = (-70 ± √(4900 + 256)) / (-32)
t = (-70 ± √(5156)) / (-32)
t = (-70 ± 71.84) / (-32)
Now, we'll calculate the two possible values of t:
t1 = (-70 + 71.84) / (-32)
t1 = 1.84 / (-32)
t1 ≈ -0.06 (rounded to two decimal places)
t2 = (-70 - 71.84) / (-32)
t2 = -141.84 / (-32)
t2 ≈ 4.43 (rounded to two decimal places)
Since time cannot be negative in this context, we discard the negative value.
Therefore, it will take approximately 4.43 seconds for the ball to hit the ground.
a baseball is hit into the air and its height h in feet after t seconds is given by h(t) = -16t62 + 64t +2
A. What is the height of the baseball when it is hit?
B. After, how many seconds does the baseball reach it's maximum height?
C. Determine the maximum height of the baseball.