Question 495056
You want to throw a ball vertically upwards so that it will go up 50 meters before turning around. What initial velocity do you have to give it?
<pre>
We use the formula for the final velocity in terms of the 
initial velocity and height:

v<sub>F</sub>² = v<sub>0</sub>² - 19.6h

where v<sub>0</sub> represents the original velocity and
v<sub>F</sub> represents the final velocity. 


When the ball reaches its maximum height it must stop at that instant
as it turns around, so we use 

v<sub>F</sub> = 0 and h = 50, and solve for v<sub>0</sub>


v<sub>F</sub>² = v<sub>0</sub>² - 19.6h

0² = v<sub>0</sub>² - 19.6(50)

 0 = v<sub>0</sub>² - 980

980 = v<sub>0</sub>² 

Taking positive square roots of both sides:

31.3 = v<sub>0</sub>

So the answer is about 31.3{{{m/s}}}

Edwin</pre>