Answer:
It takes 3 second(s) for the baseball to reach its maximum height.
The maximum height obtained by the baseball is 45.1 meters.
Explanation:
We know that time (t) in seconds is plotted on the x-axis and height (h) in meters is plotted on the y-axis.
Thus, we can find:
- the time it takes for the baseball to reach its maximum height in seconds,
- and the maximum height itself in meters
By finding both the x and y-coordinate of the maximum.
Finding the x-coordinate of the maximum:
The function h(t) = -4.9t^2 + 29.4t + 1 is in the standard form of a quadratic function, whose general equation is given by:
f(x) = ax^2 + bx + c, where
- a, b, and c are constants.
Thus, -4.9 is our a value, 29.4 is our b value, and 1 is our c value.
We can find the x-coordinate of the maximum using the formula:
x-coordinate = -b/2a
Thus, we can plug in 29.4 for b and -4.9 for a:
x-coordinate = -29.4 / 2(-4.9)
x-coordinate = -29.4 / -9.8
x-coordinate = 3
Thus, it takes 3 seconds for the baseball to reach its maximum height.
Finding the y-coordinate of the maximum:
- We know that the formula -b/2a gives us the x-coordinate of the maximum.
Thus, we can find the y-coordinate of the maximum by plugging in -b/2a for t in h(t) = -4.9t^2 + 29.4t + 1.
In this case, we substitute -29.4 / 2(-4.9) for t:
h(-b / 2a) = -4.9(-29.4 / 2(-4.9))^2 + 29.4(-29.4 / 2(-4.9)) + 1
h(-b / 2a) = -4.9(-29.4 / -9.8)^2 + 29.4(-29.4 / -9.8) + 1
h(-b / 2a) = -4.9(3)^2 + 29.4(3) + 1
h(-b / 2a) = -4.9(9) + 88.2 + 1
h(-b / 2a) = -44.1 + 88.2 + 1
h(-b / 2a) = 44.1 + 1
h(-b / 2a = 45.1
Thus, the maximum height obtained by the baseball is 45.1 meters.