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It takes ___ second(s) for the baseball to reach its maximum height.

(Round to one decimal place as needed)

The maximum height obtained by the baseball is ___ meters.
(Round to three decimal places as needed.)

It takes ___ second(s) for the baseball to reach its maximum height. (Round to one-example-1
User Zoomba
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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.

User Adam Florin
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