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  • Two projectiles are projected at two different angles . If   <img alt="h_1 \; \; and \; \; h_2" src="https://entrancecorner.oncodecogs.com/gif.latex?h_1%20%5C%3B%20%5C%3B%20and%20%5C

Two projectiles are projected at two different angles . If   h_1 \; \; and \; \; h_2  are maximum height when the range in the two cases is R , then the relation between R , h_1 \; \; and \; \; h_2 is

Option: 1

R= 4\sqrt{h_1h_2}


Option: 2

R= 2\sqrt{h_1h_2}


Option: 3

R= \sqrt{h_1h_2}


Option: 4

none of these 


Answers (1)

best_answer

 R = \frac{u^2 \sin2 \theta }{g}

R will be the same for \theta \; and \; 90 - \theta

\therefore h_1= \frac{u^2\sin ^2\theta }{2g}\; \; and\; \; h_2 = \frac{u^2\sin ^2(90-\theta )}{2g} = \frac{u^2\cos ^2\theta }{2g}

h_1h_2 = \frac{(u^2)^2\sin ^{2}\theta \cdot \cos ^{2}\theta }{4g^2}= \frac{\left [ (u^2)(2\sin \theta \cdot \cos \theta) \right ]^2 }{16g^2}= \left [\frac{ (u^2)^2(\sin2\theta)^2 }{g^2} \right ]\cdot \frac{1}{16}

R^2 =16 h_1h_2   or R =4 \sqrt{h_1h_2}

Posted by

manish painkra

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