A ball strikes a wall with a velocity u at an angle - with the normal to the wall surface and rebounds from it at an angle - with the surface- Then-A- -90- if wall is smoothB- If the wall is smooth- coefficient of restitution -tan-C- If wall is smooth- coefficient of restitution -tan-D- none of these

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The 'e' Equation

A ball strike...

Question

A ball strikes a wall with a velocity $\to u$ at an angle $θ$ with the normal to the wall surface and rebounds from it at an angle $β$ with the surface. Then:

> , if wall is smooth

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If the wall is smooth, coefficient of restitution

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If wall is smooth, coefficient of restitution <

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none of these

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Solution

The correct option is B
If the wall is smooth, coefficient of restitution

Velocity v cos $β$ = u sin $θ$ . . . (i)

$v s i n β = e . u ‘ c o s θ$ . . . (ii)

from the above equation, tan $β = e c o t θ$

$o r t a n β = e t a n (90^{\circ} - θ)$

$β < (90 - θ)$

$o r (β + θ) < 90^{\circ}$

$e = \frac{t a n β}{t a n θ}$ , Hence, (b) is the correct choice

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A ball strikes a wall with a velocity →u at an angle θ with the normal to the wall surface and rebounds from it at an angle β with the surface. Then:

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A ball strikes a wall with a velocity $\to u$ at an angle $θ$ with the normal to the wall surface and rebounds from it at an angle $β$ with the surface. Then: