Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is π /3 and its maximum height is y 1 then the

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Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is π /3 and its maximum height is y 1 ​ then the maximum height of the other will be -

TestHub · Accepted Answer

To have equal ranges for the same initial speed, the angles of projection must be complementary, i.e., $θ_{1} + θ_{2} = π /2$ .

Given $θ_{1} = π /3$ , then $θ_{2} = π /2 - π /3 = π /6$ .

The maximum height is $H = \frac{u ^{2} s i n ^{2} θ}{2 g}$ .

So, $y_{1} = \frac{u ^{2} s i n ^{2} ( π /3 )}{2 g}$ and $y_{2} = \frac{u ^{2} s i n ^{2} ( π /6 )}{2 g}$ .

$\frac{y _{2}}{y _{1}} = \frac{s i n ^{2} ( π /6 )}{s i n ^{2} ( π /3 )} = \frac{( 1/2 ) ^{2}}{( 3 /2 ) ^{2}} = \frac{1/4}{3/4} = 1/3$ .

Thus, $y_{2} = y_{1} /3$ .

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