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3-2.Motion in Plane
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A ball is thrown at different angles with the same speed $u$ and from the same point. It has the same range in both cases. If $y_1$ and $y_2$ be the heights attained in the two cases, then $y_1+y_2$ equals to
A
$\frac{{{u^2}}}{g}$
B
$\frac{{2{u^2}}}{g}$
C
$\frac{{{u^2}}}{{2g}}$
D
$\frac{{{u^2}}}{{4g}}$
Solution
$\theta , 90^o -\theta $
${y_1} = \frac{{{u^2}{{\sin }^2}\theta }}{{2g}}$ and ${y_2} = \frac{{{u^2}{{\cos }^2}\theta }}{{2g}}$
$\therefore {y_1} + {y_2} = \frac{{{u^2}{{\sin }^2}\theta }}{{2g}} + \frac{{{u^2}{{\cos }^2}\theta }}{{2g}}$
$\therefore {y_1} + {y_2} = \frac{{{u^2}}}{{2g}}$
Standard 11
Physics
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