Jules kicks a soccer ball off the ground and into the air with an initial velocity of 25 feet per second. Assume the starting height of the ball is 0 feet. Approximatly how long does it take until the soccer ball hits the ground again?

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The equation is h(t) = at^2 + vt + d

where a = acceleration of gravity = - 32.174 ft/sec^2

v = 25 feet/sec

d = starting height = 0

and h(t) = 0 when the ball hits the ground.

So, 0 = - 32.174t^2 + 25t + 0

You can use the quadratic formula on that if you want, or you can solve like this:

0 = - 32.174t^2 + 25t

So, one solution of that is t = 0, corresponding to the initial time when the ball is kicked.

The other time is: 25 = 32.174t

t = 25/32.174 = 0.777 seconds

or approximately 0.8 seconds.

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