Question

A construction worker's helmet slips and falls when he is 78.4m above the ground, he hears the sound of the helmet hitting the ground 4.23s after it slipped.Find the speed of the speed of sound in air.

Answer 1

$$\begin{gathered} \mathrm{Case}\mathrm{I}:\left(\mathrm{Time}\mathrm{taken}\mathrm{by}\mathrm{helmet}\mathrm{to}\mathrm{reach}\mathrm{ground}\right) \\ {\mathrm{t}}_1=\sqrt{\frac{2\mathrm{h}}{\mathrm{g}}} \\ =\sqrt{\frac{2\times 78.4}{9.8}} \\ =4\mathrm{s} \\ \mathrm{Case}\mathrm{II}:\left(\mathrm{Time}\mathrm{taken}\mathrm{by}\mathrm{sound}\mathrm{to}\mathrm{reach}\mathrm{the}\mathrm{wroker}\mathrm{from}\mathrm{the}\mathrm{ground}\right) \\ {\mathrm{t}}_2=\frac{\mathrm{h}}{\mathrm{v}} \\ =\frac{78.4}{\mathrm{v}} \\ \mathrm{Total}\mathrm{time}\mathrm{taken},\mathrm{t}=4.23\mathrm{s} \\ \mathrm{Hence},{\mathrm{t}}_2=\mathrm{t}-{\mathrm{t}}_1 \\ =4.23-4 \\ =0.23\mathrm{s} \\ \mathrm{Velocity}\mathrm{of}\mathrm{sound}: \\ \mathrm{v}=\frac{78.4}{{\mathrm{t}}_2} \\ =\frac{78.4}{0.23} \\ =340.9\mathrm{m}/\mathrm{s} \end{gathered}$$