Question 75081
<pre><font size = 5><b>
A ball is thrown upward from the roof of a 
building 100 m tall with an initial velocity
of 20 m/s. When will the ball reach a height
of 80 m?  Please show work.


The formula is

                h = h<sub>O</sub> + v<sub>O</sub>t - 4.9t²

where
h = final height in m, which here is 80m
h<sub>O</sub> = initial height in m, which here is 100m
v<sub>O</sub> = initial velocity in m/s, which here is +20m/s
     (+ because it's upward)
t = final time in s, which is what we need to find.

                h = h<sub>O</sub> + v<sub>O</sub>t - 4.9t²

               80 = 100 + 20t - 4.9t²

 4.9t² - 20t + 80 = 100

 4.9t² - 20t - 20 = 0

49t² - 200t - 200 = 0

Use the quadratic formula:
                  ______ 
            -b ± <font face = "symbol">Ö</font>b²-4ac
        x = —————————————
                2a 

where a = 49; b = -200; c = -200

                        ___________________ 
             -(-200) ± <font face = "symbol">Ö</font>(-200)²-4(49)(-200)
        x = ————————————————————————————————
                       2(49) 
                    ___________ 
             200 ± <font face = "symbol">Ö</font>40000+39200
        x = ————————————————————
                     98

                    _____ 
             200 ± <font face = "symbol">Ö</font>79200
        x = ——————————————
                   98

                    _______ 
             200 ± <font face = "symbol">Ö</font>3600·22
        x = ———-—————————————
                   98 

                      __
             200 ± 60<font face = "symbol">Ö</font>22
        x = —————————————
                  98


                       __
             20(10 ± 3<font face = "symbol">Ö</font>22)
        x = ———————————————
                  98

             10        __       
             <s>20</s>(10 ± 3<font face = "symbol">Ö</font>22)
        x = ———————————————
                  <s>98</s>
                  49

                       __
             10(10 ± 3<font face = "symbol">Ö</font>22)
        x = ———————————————
                  49

Using the +
                       __
             10(10 + 3<font face = "symbol">Ö</font>22)
        x = ———————————————
                  49      

        x = 4.912399445

Using the -
                       __
             10(10 - 3<font face = "symbol">Ö</font>22)
        x = ———————————————
                  49      

        x = -0.8308667917

which we discard since we can't have negative time.
So the answer rounded to the nearest tenth is
4.9 seconds. 
                 
Edwin</pre>