Posted by admin on Thursday, August 12, 2010 · Leave a Comment
its a mechanic question ive tried various times but i cant do it.
the nozzle of a fountain projects a jet of water with speed 10.6m/s at 70 degrees to the horizontal. the water is caught in a cup at 4.2 metres above the level of the nozzle. calculate the time taken by the water to reach the cup.
The question is really asking how much time has passed when y = 4.2m. Note that since there is no symmetry in this problem you cannot just solve for the time when the vertical velocity is zero and just double it. Instead, use the formula
y = 1/2 ayt² + v0yt + y0
4.2 = 1/2 (-9.81)t² + 9.96t + 0
4.2 = -4.905t² + 9.96
-4.905t² + 9.96 - 4.2 = 0
Now simply use the quadratic formula and reject the negative time if one exists.
However, there can only be one time since you want the water to fall into the cup so the answer is 1.43 s. At .6s the water is at the same height as the cup going up, but it did not yet reach the cup.
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