A ball is thrown upwards from the ground with a speed of 80 ft/s. If the height of the ball is given by the function h = 80t − 16t², where t is the time in seconds. What is the maximum height that the ball will reach?1 pointA. 100 ftB. 120 ftC. 128 ftD. 132 ft
Question
A ball is thrown upwards from the ground with a speed of 80 ft/s. If the height of the ball is given by the function h = 80t − 16t², where t is the time in seconds. What is the maximum height that the ball will reach?1 pointA. 100 ftB. 120 ftC. 128 ftD. 132 ft
Solution
The maximum height of the ball can be found by finding the vertex of the parabola represented by the equation h = 80t - 16t².
The t-coordinate of the vertex of a parabola given by the equation y = ax² + bx + c is given by -b/2a.
In this case, a = -16 and b = 80.
So, t = -b/2a = -80/(2*-16) = 2.5 seconds.
Substitute t = 2.5 into the equation to find the maximum height:
h = 802.5 - 162.5² = 200 - 100 = 100 ft.
So, the maximum height that the ball will reach is 100 ft.
Therefore, the answer is A. 100 ft.
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