A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second. After how many seconds does the ball attain its maximum height?

2.87 sec

3.44 sec

4.65 sec

5.41 sec

3.44 sec It is launched vertically with an initial speed of 110 ft/sec._x000D_ It will reach maximum height when the speed drops to 0._x000D_ Vo = 110 feet per second_x000D_ ho = 2 feet_x000D_ So, h(t) = -16t^2 +110t +2_x000D_ Take the derivative: h'(t) = 110 -32t_x000D_ The maximum height will be at the inflection when the derivative crosses the x-axis, then h'(t)=0._x000D_ So, set h'(t)=0 and solve for t:_x000D_ 0 = 110 -32t_x000D_ -110 = -32t_x000D_ t = 3.4375_x000D_ t = 3.44 seconds.

Physics Author: rikazzz

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A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second. After how many seconds does the ball attain its maximum height?

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