# Simple Projectile Motion Question

A volcano erupts 50m below the sea level. A rock leaves the crater at 20 m/s at an angle 30 deg with the vertical line. The rock has a mass of 15kg. IGNORE WATER RESISTANCE. It gets out of the water, reaches a max height and falls back it.

When does it reach 30 below sea for the first and second times?

$a = <0, -9.8>$

$v = <20sin(30), -9.8t+20cos(30)> = <10, -9.8t+17.32>$

$s = <10t, -4.9t^2+17.32t>$

For the object to be 30m below sea level, y=20m, so $s_y=20 \implies -4.9t^2+17.32t-20=0$.

However, no real solutions exist to this. This is so simple, I apologize for asking, but what am I overlooking?

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Where is the volume of the rock? – Pygmalion Apr 18 '12 at 20:44
What do you mean by "$s=\langle 10t,-4.9\,t^2+17.32\,t\rangle$"? It doesn't fit dimensionally. — EDIT ok I see none of this fits dimensionally, you seem to assume units with $[s]=[t]$. – leftaroundabout Apr 18 '12 at 20:44
@Pygmalion, it's not given. – Brandon Amos Apr 18 '12 at 20:47

Right, and it can easily be seen by noting $|\mathbf{v}|^2/2<h\cdot g$. – leftaroundabout Apr 18 '12 at 20:52