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  • A stone is projected at angle  to the horizontal. The ratio of the kinetic energy of the stone

A stone is projected at angle 30^{\circ} to the horizontal. The ratio of the kinetic energy of the stone at the point of projection to its kinetic energy at the highest point of flight will be –
 

Option: 1

1 : 2 


Option: 2

1 : 4 


Option: 3

4 : 1 


Option: 4

4 : 3


Answers (1)

best_answer

\begin{aligned} & \mathrm{K}_{\mathrm{A}}=\frac{1}{2} \mathrm{mV}_{\mathrm{A}}^2 \\ & \mathrm{~K}_{\mathrm{A}}=\frac{1}{2} \mathrm{mV}_0^2 \\ & \mathrm{~K}_{\mathrm{B}}=\frac{1}{2} \mathrm{~m}\left(\mathrm{~V}_0 \cos 30^{\circ}\right)^2 \\ & \mathrm{~K}_{\mathrm{B}}=\frac{\mathrm{m}}{2} \cdot \mathrm{V}_0^2 \frac{3}{4}=\frac{3}{8} \mathrm{mV}_0^2 \\ & \frac{\mathrm{K}_{\mathrm{A}}}{\mathrm{K}_{\mathrm{B}}}=\frac{\left(\frac{\mathrm{mV}_0^2}{2}\right)}{\left(\frac{3 \mathrm{mV}_0^2}{8}\right)} \\ & \frac{\mathrm{K}_{\mathrm{A}}}{\mathrm{K}_{\mathrm{B}}}=\frac{4}{3} \\ & \end{aligned}

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