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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
For a given velocity, a projectile has the same range $R$ for two angles of projection if $t_1$ and $t_2$ are the times of flight in the two cases then
  • A
    ${t_1}{t_2} \propto \,{R^2}$
  • ✓
    ${t_1}{t_2} \propto \,R$
  • C
    ${t_1}{t_2} \propto \,\frac{1}{R}$
  • D
    ${t_1}{t_2} \propto \,\frac{1}{{{R^2}}}$
✓

Answer

Correct option: B.
${t_1}{t_2} \propto \,R$
b
(b) For same range angle of projection should be $\theta$ and $90-\theta$

So, time of flights ${t_1} = \frac{{2u\sin \theta }}{g}$ and

${t_2} = \frac{{2u\sin (90 - \theta )}}{g} = \frac{{2u\cos \theta }}{g}$

By multiplying$ = {t_1}{t_2} = \frac{{4{u^2}\sin \theta \cos \theta }}{{{g^2}}}$

${t_1}{t_2} = \frac{2}{g}\frac{{({u^2}\sin 2\theta )}}{g} = \frac{{2R}}{g}$

$⇒$ ${t_1}{t_2} \propto R$

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