Answer
a. The telescope's angular momentum is conserved (does not change) because no net external torque acts on it.
The angular momentum is mvL.
$$(m)(v_{initial})(L) = (m)(v_{new})(0.33L)$$
$$v_{new} =(v_{initial})\frac{L}{0.33L} = 3.0 v_{initial} $$
b. Plug in values.
$$v_{new} =( 1.0 \frac{m}{s})\frac{L}{0.33L} = 3.0 \frac{m}{s} $$
