Question 202853: If a juggler can toss a ball into the air with a velocity of 64ft/sec from a height of 6 ft, then what is the maximum height reached by the ball?
Found 2 solutions by Earlsdon, Edwin McCravy:
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! The height (h) of an object propelled upwards as a function of time (t) is given by:
 where g, the constant of acceleration due to gravity is 32ft/sec^2,  is the initial upwards velocity, and  is the initial height of the object.
In this problem,  ft/sec. and  ft.
Making the appropriate substitutions into the function above, we get:
This equation, when graphed, is a parabola that opens downwards, so we are looking for the maximum point (the vertex) on the curve which will give us the maximum height attained by the juggler's ball.
The value of the independent variable (t in this case) at the vertex is given by:
 where b = 64 and a = -16.
 seconds. This is the time, t, at which the juggler's ball reaches its maximum height. To find the actual maximum height, we substitute t = 2 into the function above and solve for h.
 Evaluate.
The maximum height reached by the ball is 70 feet.
Answer by Edwin McCravy(20060)  (Show Source):
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