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3.2 , motion in plane — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics3.2 , motion in plane1 Mark
MCQ
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
    $\frac{{2{u^2}}}{g}$
  • ✓
    $\frac{{{u^2}}}{{2g}}$
  • D
    $\frac{{{u^2}}}{{4g}}$
✓

Answer

Correct option: C.
$\frac{{{u^2}}}{{2g}}$
c
$\theta , 90^o -\theta $

${y_1} = \frac{{{u^2}{{\sin }^2}\theta }}{{2g}}$ and ${y_2} = \frac{{{u^2}{{\cos }^2}\theta }}{{2g}}$

$\therefore {y_1} + {y_2} = \frac{{{u^2}{{\sin }^2}\theta }}{{2g}} + \frac{{{u^2}{{\cos }^2}\theta }}{{2g}}$

$\therefore {y_1} + {y_2} = \frac{{{u^2}}}{{2g}}$

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