Answer
The acceleration due to gravity on Planet X is $1.29~m/s^2$
Work Step by Step
Let $h$ be the height of the table.
We can find the time for the ball to fall to the floor on the earth.
$h = \frac{1}{2}gt^2$
$t = \sqrt{\frac{2h}{g}}$
We can express $D$ in terms of $v_0$ and $t$.
(equation 1): $D = v_0~t = v_0~\sqrt{\frac{2h}{g}}$
Similarly, on Planet X:
(equation 2): $2.76D = v_0~\sqrt{\frac{2h}{g_x}}$
We can divide equation 1 by equation 2.
$\frac{D}{2.76D} = \frac{v_0~\sqrt{\frac{2h}{g}}}{v_0~\sqrt{\frac{2h}{g_x}}}$
$\frac{1}{2.76} = \sqrt{\frac{g_x}{g}}$
$g_x = g~(\frac{1}{2.76})^2 = (9.80~m/s^2)(\frac{1}{2.76})^2$
$g_x = 1.29~m/s^2$
The acceleration due to gravity on Planet X is $1.29~m/s^2$
