Question

If a baseball player hits a baseball from 4 feet off the ground with an initial velocity of 64 feet per second, how long will it take the baseball to hit the ground? Use the equation h = −16t2 + 64t + 4.

Answer 1

Answer: 2 plus or minus square root of 17 end root over 2

Answer 2

4.0616 seconds approximately

Explanation:

We are looking for how long it takes the ball to hit the ground. h is 0 then.

So we are looking to solve -16t^2+64t+4=0

Divide both sides by -4 to make the numbers a little simpler to work with.

4t^2-16t-1=0

You could aim for completing the square or quadratic formula here.

I'm going for quadratic formula.

a=4

b=-16

c=-1

So the discriminant=b^2-4ac=(-16)^2-4(4)(-1)=16^2+16=16(16+1)=16(17)=272

You could have just put (-16)^2-4(4)(-1) into your calculator.

The quadratic formula says to do:

-b plus or minus square root (discriminant)

-------------------------------------------------------------

2 times a

=

16 plus or minus sqrt(272)

-------------------------------------

8

=(approximately)

16 plus or minus 16.4924

-----------------------------------

8

=

16+16.4924 16-16.4924

---------------- or ----------------

8 8

=

32.4924 -0.4924

------------- or -----------

8 8

=

4.0616 or -0.062

So the baseball hits the ground 4.0616 seconds approximately after the ball has been hit.