SOLUTION: 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?

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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(20056)   (Show Source): You can put this solution on YOUR website!
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?



where  = the final velocity
where  = the initial velocity 

(that's the speed at which the ball was thrown 
upward at the beginning, which is 64 ft/sec)

The ball has to stop momentarily when it gets to its maximum height.

 = the number of seconds it takes the ball to 
change its speed from ft/sec to   

Therefore  = 0

Substituting into









.

So it reaches its maximum height in 2 seconds.

Now we use another formula to find out how high the
ball was exactly 2 seconds after it was thrown up:



 = the height of the ball at time t

 = the initial height 

(that's the height of ball at beginning of the toss, feet

and where  = the initial velocity = ft/sec

(that's the height of ball at beginning of toss)

Substitute , , 

in:











So the maximum height of the ball is 70 feet

Edwin
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