#### Answer

(a) $U_0 = 2.16~J$
(b) The 25-g pebble could go up to a height of 8.8 meters.
(c) We ignored air resistance in solving this question.

#### Work Step by Step

The initial potential energy stored in the slingshot will be equal to the potential energy of the pebble at maximum height.
(a) $U_0 = mgh = (0.010~kg)(9.80~m/s^2)(22.0~m)$
$U_0 = 2.16~J$
(b) $mgh = U_0$
$h = \frac{U_0}{mg} = \frac{2.16~J}{(0.025~kg)(9.80~m/s^2)}$
$h = 8.8~m$
The 25-g pebble could go up to a height of 8.8 meters.
(c) We ignored air resistance in solving this question.