Question

In a ballistic pendulum experiment, projectile 1 results in a max height,h, of the pendulum equal to 2.6cm. A second projectile (of the same mass) causes the pendulum to swing twixe as high, h2 = 5.2cm. The second projectile was how many times faster than the first?

Answer 1

If energy is conserved, you end up with:
\[v = \sqrt{2gh}\]
So, if you double the height (h) and do not change the acceleration due to gravity (g), how much would the velocity increase?