Solve for t when the object hits the ground. Fill in the blanks of the quadratic formula.

Question

If an object is thrown vertically upward with an initial velocity of v, from an originial position of s, the height h at any time t is given by 

h = -16t^2 +vt + s (where h and s are in ft, t is in seconds and v is in ft/sec.) (when h = 0) 

t=blank1+-sqrt(blank2-4(blank3))

   __________________________

                   2(-16)

Fill in the blanks of the quadratic formula. Blank 1, Blank 2, and Blank 3

Answer 1

Hi Kehli, so this question is asking you to complete the quadratic formula for an equation modeling the height of an object thrown vertically upwards.

 

Here is that equation:

h = -16t^2 +vt + s

 

The first step is to recognize what the quadratic formula is. Simply put, we use the quadratic formula to find solution(s) of a quadratic equation. As you may know, a quadratic equation is any equation in which the highest power of the variable in the equation is 2.

 

The general quadratic equation is ax^2+bx+c = 0.

Quadratic equations can also be solved using factoring, completing the square, and graphing, but here, the question asks us to use the method of the quadratic formula. This formula is:

 

x = [ -b ± sqrt(b^2 - 4ac) ] / 2a

 

where a, b, and c refer to the coefficients in the general equation bolded above.

 

So now, we need to identify what a, b, and c are in the equation that your problem gives. The "t" variable is taking the place of the "x" variable in the general quadratic equation. This means:

a = -16

b = v

c = s

 

Your final quadratic expression will look like this:

 

t = [ -v ± sqrt(v^2 - 4(-16)(s) ] / 2(-16)

 

I hope this helps, and feel free to respond with any follow up questions!

Answer 2

h(t) = -16t² + vt + s

 

When h(t) = 0

 0 = -16t² + vt + s

 

For a general quadratic equation of the form:

 

0 = at² + bt + c

 

You can solve for t using the quadratic formula:

 

       -b ± √(b²-4ac)

t = ---------------------

              2a

 

In your case, a = -16, b = v, c = s.  Substitute those values in place of a, b, and c in the quadratic formula.

 

      -v ± √(v²-4(-16)(s))      blank1 ± √(blank2 - 4*blank3)
t = -------------------------- =  -------------------------------------------------
              2(-16)                                            2(-16)

 

So:

Blank 1 = -b = -v

Blank 2 = b² = v²

Blank 3 = a*c = -16s