Let us consider the air with the index 1 and the lucite with index 2. Using the Snell's Secound Law, we have:
Entering the unknowns, remembering that the air refrective index is 1 and the lucite refrective index is 1.5, comes:
Using the arcsin properties, we get:

Obs: Approximate results, and the drawing is attached
If you notice any mistake in my english, let me know, because i am not native.
Answer:
6 seconds
0.167 Hz
Explanation:
Distance = 4 m
Velocity = 0.75 m/s
Period is given by

The period of the motion is 3 seconds
Frequency is given by

The frequency of the motion is 0.33 Hz
Actual velocity of the ping-pong ball= 5 m/s
Explanation:
velocity of ping pong ball because of the shot gun= 4 m/s North
velocity added to the ping-pong ball due to the wind=3 m/s
These velocities are perpendicular to each other. so we use Pythagoras theorem to find the resultant velocity of the ping- pong ball
so the actual velocity of the ping-pong ball =V= √4²+3²
V= √25
V= 5 m/s