Capturing the sampling rate from a basketball being dribbled
The information you are given is $f_\textrm{bounce} = 1\,\textrm{Hz}$ - all the technical details about the sine wave and its amplitude is irrelevant. Please note that frequency is always measured in something happening per second, i.e. the unit is always $\frac{1}{\textrm{s}}$.

Since you do not want to have an answer, I try to give you a hint:


Imagine you had a camera that would capture an image once a second. Assume that the moment the image is taken is always when the basketball exactly in the middle between the floor and the player's hand. What can you say about the motion of the basketball after having watched this video?
Imagine your camera would capture the scene every $0.5\,\textrm{s}$, i.e. the frame rate would be $2f_\textrm{bounce} = 2\,\textrm{Hz}$, again exactly when the basketball is between the player's hand and the floor. What would be the difference between this video and the first video? What would you learn about the motion of the basketball by watching this video?


If you want to get more information, you could search for the Nyquist–Shannon sampling theorem.