Question

A ball is thrown into the air with an upward velocity of 36ft/s. Its height h in feet after t seconds is given by the function h = -16t^2 +36t+ 9. In how many seconds does the ball reach its maximum

Answer 1

To determine the time it takes for the ball to reach its maximum height, we need to find the vertex of the quadratic function representing the height of the ball. The vertex represents the highest point on the parabolic path of the ball.

The equation representing the height of the ball as a function of time is given by h = -16t^2 + 36t + 9, where h is the height in feet and t is the time in seconds.

The general form of a quadratic equation is y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = -16, b = 36, and c = 9.

The x-coordinate of the vertex can be found using the formula x = -b / (2a). Substituting the values, we have:

x = -36 / (2 * -16)

x = -36 / -32

x = 1.125

Therefore, it takes approximately 1.125 seconds for the ball to reach its maximum height.

Explanation:

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