Question 1034139
.
Please help me solve this problem. I know the answer is after about 1.75 seconds, but I do not know the steps to get that answer. ...
We are studying projectile motion. Maddie served a volleyball from 1 meter off the ground with an upward velocity of 8 meters per second. 
If no-one touches the ball, when will it hit the ground?
Thanks in advance!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
Only vertical component of the velocity is relevant to this problem.

The equation describing the height of the ball above the ground in this problem is

{{{(-9.8/2)t^2 + 8t + 1}}} = {{{0}}},  or  (which is the same)

{{{-4.9t^2 + 8t + 1}}} = {{{0}}}.     (1)

Here t is the time the volleyball is in the air, and {{{0}}} in the right side is the ground level.

Solve this quadratic equation for t, and choose an appropriate root.


Now a bit more explanation.
If the object is thrown vertically with the initial vertical velocity "v" from the initial height {{{h[0]}}}, its height h(t) is a quadratic function

h(t) = {{{-(gt^2)/2 + vt + h[0]}}}.    (2)

It will hit the ground when h(t) = 0.

Here "g" is the gravity acceleration, also known as "free fall acceleration"

The value for g is about 9.81 {{{m/s^2}}} near the Earth surface.

Based on this info, the equations (1) and (2) above are written.

Now solve the quadratic equation (1) and get your answer.


What I explained to you, is part of Physics. 
In this compact form it is necessary information for solving this kind of problems in Algebra.
</pre>

Good luck!

If you have questions, don't hesitate to ask in this site.



This plot shows you the height of the ball above the ground as a function of time.


Can you see from the plot WHEN the volleyball will hit the ground?


<TABLE> 
  <TR>
  <TD> 

{{{graph( 330, 330, -2.5, 5.5, -0.5, 5.5,
          -(9.8/2)x^2 + 8x + 1
)}}}


<B>Figure</B>. Plot h(t) = {{{-(9.8/2)t^2 + 8t + 1}}}

  </TD>
  </TR>
</TABLE>