> Q. Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is $pi/3$ and the maximum height reached by it is 102 metres. Then the maximum height reached by the other in metres is – LIVE ANSWER TODAY

Q. Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is $pi/3$ and the maximum height reached by it is 102 metres. Then the maximum height reached by the other in metres is

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Two stones are projected with the same speed but making different angles with the horizontal. Their horizontal ranges are equal. The angle of projection of one is $pi/3$ and the maximum height reached by it is 102 metres. Then the maximum height reached by the other in metres is

Solution:

Given $theta_{1}=pi/3=60^{circ}$

Horizontal range is same for the angle of projection

$theta$ or $90-theta$

$therefore theta_{2}=90-theta_{1}=90^{circ}-60^{circ}=30^{circ}$

$therefore$ Maximum height $H=frac{u^{2},sin^{2}theta}{2g}$

$ therefore frac{H_{1}}{H_{2}}=frac{frac{u^{2},sin^{2},theta_{1}}{2g}}{frac{u^{2},sin^{2},theta_{2}}{2g}}$

$=frac{sin^{2},theta_{1}}{sin^{2},theta_{2}}=frac{sin^{2},60^{circ}}{sin^{2},30^{circ}}$

$=frac{left(sqrt{3}2right)^{2}}{left(1 2right)^{2}}$

$thereforefrac{H_{1}}{H_{2}}=3$ or, $H_{2}=frac{H_{1}}{3}=frac{102}{3}$

(given $H_{1}=102,m)$

$=34,m$

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