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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
An object is projected in the air with initial velocity $u$ at an angle $\theta$. The projectile motion is such that the horizontal range $R$, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be $.......$ degree.
  • A
    $85$
  • B
    $80$
  • ✓
    $15$ or $75$
  • D
    $70$
✓

Answer

Correct option: C.
$15$ or $75$
c
$R _{\max }=\frac{ u ^{2} \sin 2\left(45^{\circ}\right)}{ g }=\frac{ u ^{2}}{ g }$

$\frac{ R }{2}=\frac{ u ^{2}}{2 g }=\frac{ u ^{2} \sin 2 \theta}{ g }$

$\sin 2 \theta=\frac{1}{2}$

$2 \theta=30^{\circ}, 150^{\circ}$

$\theta=15^{\circ}, 75^{\circ}$

Ans. $15, 75$

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