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how long does it ake the ball to get to the basket?

 

f(t)=-16t^2+27t+6

 May 22, 2017
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Solve for t:
-16 t^2 + 27 t + 6 = 0

Divide both sides by -16:
t^2 - (27 t)/16 - 3/8 = 0

Add 3/8 to both sides:
t^2 - (27 t)/16 = 3/8

Add 729/1024 to both sides:
t^2 - (27 t)/16 + 729/1024 = 1113/1024

Write the left hand side as a square:
(t - 27/32)^2 = 1113/1024

Take the square root of both sides:
t - 27/32 = sqrt(1113)/32 or t - 27/32 = -sqrt(1113)/32

Add 27/32 to both sides:
t = 27/32 + sqrt(1113)/32 or t - 27/32 = -sqrt(1113)/32

Add 27/32 to both sides:
Answer: | t = 27/32 + sqrt(1113)/32= ~1.886 Seconds                              or                         t = 27/32 - sqrt(1113)/32

 May 22, 2017

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