Question

I dont understand pojectile motion can someone help with this

Answer 1

When thrown from the balloon, the sandbag has a constant horizontal/forward velocity. As the text puts it, "the sandbag continues forward as if it had not been dropped." What this means is that the sandbag has no acceleration in the horizontal plane of motion, so it moves in this direction at a constant speed. So for any time $t$, the horizontal velocity is given by

$v_x(t) = 12\dfrac{\rm m}{\rm s}$

In the vertical plane of motion, the sandbag has no vertical velocity until it's released and allowed to fall. As it's falling, however, the sandbag is being pulled down by gravity and is accelerating with magnitude $g=9.8\frac{\rm m}{\mathrm s^2}$, so its vertical/downward velocity at time $t$ is given by

$v_y(t) = -gt$

So, after 3 seconds have passed, the sandbag has horizontal velocity $v_x = 12\frac{\rm m}{\rm s}$ and vertical velocity $v_y = -g(3\,\mathrm s) = -29.4\frac{\rm m}{\rm s}$. If the question is specifically asking about speed you would just ignore the negative signs.