The ranges and heights for two projectiles projected with the same initial velocity at angles $42^\circ $ and $48^\circ $ with the horizontal are $R_1\,,R_2$ and $H_1\,,H_2$ respectively. Choose the correct option: (A) $R_1 < R_2 $ and $H_1 < H_2 $ (B) $R_1 > R_2 $ and $H_1 = H_2 $ (C) $R_1 = R_2 $ and $H_1 = H_2 $ (D) $R_1 = R_2 $ and $H_1 < H_2 $ Solution $R=\frac {u^2 sin 2\theta }{g} $, $H=\frac {u^2 sin^2 \theta }{2g}$ $\frac {R_1}{R_2} = \frac {sin 2 \times 42^\circ}{sin 2\times 48^\circ} = \frac {cos 6^\circ}{cos 6^\circ} = 1 $ $\frac {H_1}{H_2}= \frac {sin^2 42^\circ }{sin^2 48^\circ } = tan^2 42^\circ < 1 $ Answer: (D)
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