Final answer:
To find the maximum height reached by the ball, the time t when the ball reaches the maximum height can be calculated using the vertex formula t = -b/(2a). Plugging the determined time back into the quadratic height equation h = 90t – 16t2 gives the maximum height. The calculated maximum height is 126.6 feet, rounded to one decimal place.
Step-by-step explanation:
To determine the maximum height that a ball reaches when it is thrown straight upward with a velocity of 90 ft/sec, where the height above the ground after t seconds is given by h = 90t – 16t2, calculus methods can be used. The height function is a quadratic equation, so the maximum height occurs at the vertex of the parabola represented by this equation. The time at which the ball reaches the maximum height, t, can be found using the formula t = -b/(2a), where a and b are the coefficients of the quadratic term and the linear term respectively.
In the given height equation h = 90t – 16t2, the coefficient a is -16 and b is 90. Substituting these values into the formula gives t = -90/(2×(-16)), which simplifies to t = 2.8125 seconds. Plugging this value back into the height equation gives the maximum height as h = 90(2.8125) – 16(2.8125)2, which calculates to approximately 126.5625 feet. Therefore, the maximum height reached by the ball is 126.6 feet, rounded to one decimal place.