Question

A block is sliding down along a smooth inclined plane when released from the top. Another block is falling freely from the same position . Which block will touch the ground earlier . Which one will hit the ground with more vel?

Answer 1

Dear student
$$\begin{gathered} ifwereleaseabodyverticallythen \\ {v}_1=\sqrt{2gh}and{t}_1=\sqrt{\frac{2h}{g}} \\ ifwereleasesamebodyoninclineplaneoflengthxmakingangle\theta withhorizontalthen \\ x=\frac{1}{2}g\sin \theta t^2 \\ \frac{h}{\sin \theta }=\frac{1}{2}g\sin \theta t^2 \\ {t}_2=\frac{1}{\sin \theta }\sqrt{\frac{2h}{g}} \\ nowspeed \\ {v}_2=\sqrt{2g\sin \theta \times x}=\sqrt{2g\sin \theta \times \frac{h}{\sin \theta }}=\sqrt{2gh} \\ wecanseethatstoppedisequalbutnottime \\ regards \end{gathered}$$