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Standard XII

Physics

Applications of Relative Projectile

A particle is...

Question

A particle is projected from surface of the inclined plane with speed $u$ and at an angle $θ$ with the horizontal. After some time the particle collides elastically with the smooth fixed inclined plane for the first time and subsequently moves in vertical direction. Starting from projection, find the time taken by the particle to reach maximum height. (Neglect time of collision).

\frac{2 u cos θ}{g}

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\frac{2 u s i n θ}{g}

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\frac{u (s i n θ + c o s θ)}{g}

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\frac{2 u}{g}

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Solution

The correct option is B $\frac{u (s i n θ + c o s θ)}{g}$
After the elastic collision with inclined plane the projectile moves in vertical direction.
The inclination of plane with horizontal is $45^{0}$ , hence velocity of particle just before collision should be horizontal.
$∴$ Time required to reach maximum height
$\Rightarrow t_{A B} + t_{B C} = \frac{u s i n θ}{g} + \frac{u c o s θ}{g}$

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