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Standard XII

Physics

Intro to Projectile on an Incline

A particle is...

Question

A particle is projected down on inclined plane with a velocity of $21 m / s$ at an angle of $60^{o}$ with the horizontal. Its range on the inclined plane, inclined at an angle of $30^{o}$ with the horizontal is

21 d m

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2.1 d m

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30 d m

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6 d m

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Solution

The correct option is D $6 d m$
Range down the plane $= \frac{2 u^{2} cos α sin (α + β)}{g {cos}^{2} β}$
$= \frac{2 \times 21 \times 21 cos 60^{o} sin 90^{o}}{10 \times {cos}^{2} 30^{o}}$
$= \frac{2 \times 441 \times \frac{1}{2}}{10 \times \frac{3}{4}} = 58.8 c m$
$= 5.88 d m ≃ 6 d m$ .

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A particle is projected down on inclined plane with a velocity of 21m/s at an angle of 60o with the horizontal. Its range on the inclined plane, inclined at an angle of 30o with the horizontal is

The correct option is D 6dmRange down the plane =2u2cosαsin(α+β)gcos2β =2×21×21cos60osin90o10×cos230o =2×441×1210×34=58.8cm =5.88dm≃6dm.

A particle is projected down on inclined plane with a velocity of $21 m / s$ at an angle of $60^{o}$ with the horizontal. Its range on the inclined plane, inclined at an angle of $30^{o}$ with the horizontal is

The correct option is D $6 d m$
Range down the plane $= \frac{2 u^{2} cos α sin (α + β)}{g {cos}^{2} β}$
$= \frac{2 \times 21 \times 21 cos 60^{o} sin 90^{o}}{10 \times {cos}^{2} 30^{o}}$
$= \frac{2 \times 441 \times \frac{1}{2}}{10 \times \frac{3}{4}} = 58.8 c m$
$= 5.88 d m ≃ 6 d m$ .