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Two stones are projected with same speed but making different angles with horizontal such that their range are same if the angle of projection of one is pi/3 and find it's max.height of second

Venkat
273 Points
3 years ago
Two stones are projected with same speed but making different angles with horizontal such that their range are same if the angle of projection of one is pi/3 and find it's max.height of second
Ans : Maxium height of second is 1/3 rd of first one. Please find the solutrion below.

$R_1=R_2 \\ \\\frac{u^2sin2\theta_1}{g}=\frac{u^2sin2\theta_2}{g} \\ \\sin2\theta_1=sin2\theta_2 \\sin\theta_1cos\theta_1=sin\theta_2cos\theta_2 \\\theta_1=60 \\sin60cos60=sin\theta_2cos\theta_2 \\\frac{\sqrt{3}}{2}\times {\frac{1}{2}}=2sin\theta_2 \\2sin\theta_2= \frac{\sqrt{3}}{4} \\\theta_2=60/2=30 \\ \\H_1=\frac{u^2sin^2\theta_1}{g}=\frac{u^2sin^260}{g}=\frac{3u^2}{8g}=y_1 \\ \\H_2=\frac{u^2sin^2\theta_2}{g}=\frac{u^2sin^230}{g}=\frac{u^2}{8g}=\frac{y_1}{3} \\H_1:H_2=1:\frac{1}{3}$