Answer
The correct answer is: (c) 3v
Work Step by Step
We can find an expression for the speed when the catapult is stretched a distance $d$:
$\frac{1}{2}mv^2 = \frac{1}{2}kd^2$
$v = d~\sqrt{\frac{k}{m}}$
We can find an expression for the speed when the catapult is stretched a distance $3d$:
$\frac{1}{2}mv_2^2 = \frac{1}{2}k(3d)^2$
$v_2 = 3\times d~\sqrt{\frac{k}{m}}$
$v_2 = 3v$
The correct answer is: (c) 3v
