Question

A small block slides without friction down the inclined plane starting from rest . let Sn be the distance travelled from t = n-1 to t= n. Then S_n/S_{n + 1} is ?

Answer 1

$$\begin{gathered} Acceleration=g\sin \theta \\ {S}_n=dis\tan cetravelledin{n}^{}seconds-dis\tan cetravelledin(n-1)seconds \\ {S}_n=un+\frac{1}{2}g\sin \theta \left(n^2\right)-u(n-1)-\frac{1}{2}g\sin \theta (n-1{)}^2 \\ {S}_n=u+\frac{1}{2}g\sin \theta (2n-1) \\ simillarlydis\tan cetravelledin(n+1{)}^{th} \\ {s}_{n+1}=u+\frac{1}{2}g\sin \theta (2n+1) \\ hereu=0 \\ \frac{s_n}{S_{n+1}}=\frac{2n-1}{2n+1} \end{gathered}$$