Answer:
6.3 seconds
Step-by-step explanation:
The time can be found by solving the equation for the time that makes the height be zero.
<h3>Equation</h3>
The equation we want to solve is ...
h(t) = 0
-16t² +100t +5 = 0 . . . . . equation for t when height is zero
<h3>Solution</h3>
We can find the solution to this equation by "completing the square."
-16(t² -6.25t) +5 = 0 . . . . factor out the leading coefficient
-16(t² -6.25t +3.125²) +5 +16(3.125²) = 0 . . . . add and subtract 16(6.25/2)²
-16(t -3.125)² +161.25 = 0
(t -3.125)² = -161.25/-16 . . . . . . subtract 161.25 and divide by -16
t = 3.125 +√(161.25/16) ≈ 6.2996
It takes about 6.3 seconds for the ball to hit the ground.
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<em>Additional comment</em>
We have ignored the negative solution, which is irrelevant to this problem.
Note that this equation for ballistic motion assumes the serve was made straight upward. The ball would reach a height of over 160 feet, given the upward initial velocity of 100 ft/s.