SOLUTION: For a typical basketball shot, the balls height (in feet) will be a function of time in flight (in seconds), models by any equations such as h= -16^2 + 40t . What is the maximum

Question 646624: For a typical basketball shot, the balls height (in feet) will be a function of time in flight (in seconds), models by any equations such as h= -16^2 + 40t .
What is the maximum height of the ball?
When will the shot reach the height of the basket (10 feet)?
When will the ball hit the floor, if it is missed the basket entirely?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
For a typical basketball shot, the balls height (in feet) will be a function of time in flight (in seconds), models by any equations such as h= -16t^2 + 40t
..
What is the maximum height of the ball?
h= -16t^2 + 40t
This is an equation of a parabola that opens downward. Curve has a maximum.
Its standard form: y=(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex. k=maximum
complete the square:
h= -16(t^2-40t/16
h= -16^2 +5t/2
h=-16(t^2-5t/2+25/16)+25
h=-16(t-5/4)^2+25
maximum height=25 ft
..
When will the shot reach the height of the basket (10 feet)?
10= -16t^2 + 40t
16t^2-40t+10=0
solve for t by following quadratic formula:

a=16, b=-40, c=10
ans:
on the way up≈0.28 sec
on the way down≈2.22 sec
..
When will the ball hit the floor, if it is missed the basket entirely?
0= -16t^2 + 40t
16t^2-40t=0
t(16t-40)=0
t=0 (reject, t>0)
or
16t-40=0
t=40/16=5/2=2.5 sec

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