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(A) For two projectiles to trace identical trajectories,their maximum heights $(H)$ and horizontal ranges $(R)$ must be equal.The formula for maximum

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$2.5$

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(A) For two projectiles to trace identical trajectories,their maximum heights $(H)$ and horizontal ranges $(R)$ must be equal.The formula for maximum height is $H = \frac{u^2 \sin^2 	heta}{2g}$.Since the trajectories are identical,the angle of projection $	heta$ is the same for both.Equating the heights: $\frac{u_1^2 \sin^2 	heta}{2g_1} = \frac{u_2^2 \sin^2 	heta}{2g_2}$.Substituting the given values ($u_1 = 10 \, m/s$,$u_2 = 5 \, m/s$,and $g_1 = 10 \, m/s^2$):$\frac{10^2}{2 	imes 10} = \frac{5^2}{2 	imes g_2}$.$\frac{100}{20} = \frac{25}{2g_2}$.$5 = \frac{12.5}{g_2}$.$g_2 = \frac{12.5}{5} = 2.5 \, m/s^2$.

Two projectiles,one fired from the surface of the Earth with velocity $10 \, m/s$ and the other fired from the surface of another planet with initial speed $5 \, m/s$,trace identical trajectories. The value of the acceleration due to gravity on the planet is ......... $m/s^2$.

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