Question

A ball is thrown straight upward with a velocity of 90 ft/sec. Its height above the ground after t seconds is h = 90t - 16t².

What is the maximum height that the ball reaches? _______ ft. Round to one decimal place

Answer 1

The maximum height reached by the ball is found using the vertex formula and plugging the time back into the height equation, resulting in a maximum height of 126.6 ft.

Step-by-step explanation:

To find the maximum height that the ball reaches, we can use the given height function h = 90t - 16t².

The maximum height occurs at the vertex of the parabola represented by this function. The t-coordinate of the vertex can be found using the formula t = -b/(2a) where a = -16 and b = 90 from the quadratic equation.

Using the formula, we get t = -90/(2×-16) = 2.8125 seconds.

Now, we plug this value back into the height function to find the maximum height: h = 90×2.8125 - 16×2.8125².

After performing the calculations, we find that the maximum height, rounded to one decimal place, is 126.6 ft.