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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

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 
 

Grade:11

1 Answers

Venkat
273 Points
5 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}

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