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Question

(A) For the first stone projected vertically upwards,the maximum height reached is $h_1 = \frac{v^2}{2g}$.The potential energy at the highest point is

Vedclass · Accepted Answer

$4:1$

Vedclass · Answer

(A) For the first stone projected vertically upwards,the maximum height reached is $h_1 = \frac{v^2}{2g}$.The potential energy at the highest point is $PE_1 = mgh_1 = mg \left( \frac{v^2}{2g} ight) = \frac{mv^2}{2}$.For the second stone,the angle with the vertical is $60^{\circ}$,which means the angle with the horizontal is $	heta = 90^{\circ} - 60^{\circ} = 30^{\circ}$.The maximum height reached by the second stone is $h_2 = \frac{v^2 \sin^2 	heta}{2g} = \frac{v^2 \sin^2 30^{\circ}}{2g} = \frac{v^2 (0.5)^2}{2g} = \frac{v^2}{8g}$.The potential energy at the highest point is $PE_2 = mgh_2 = mg \left( \frac{v^2}{8g} ight) = \frac{mv^2}{8}$.The ratio of their potential energies is $\frac{PE_1}{PE_2} = \frac{mv^2/2}{mv^2/8} = \frac{8}{2} = 4:1$.

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