A particle is projected with a velocity - u- making anangle - - with the horizontal- At any instant- its nbsp-velocity - v- is at right angles to its initial velocity - u- nbsp-then - v- is- u- - cot - u- - sec - u- - tan - u- - cos -

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A particle is...

Question

A particle is projected with a velocity $u$ making anangle $θ$ with the horizontal. At any instant, its velocity $v$ is at right angles to its initial velocity $u$ ; then $v$ is:

u

c o s θ

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u

t a n θ

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u

c o t θ

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u

s e c θ

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Solution

The correct option is A $u$ $c o t θ$
Since the new velocity is perpendicular to the initial velocity and the initial velocity makes an angle $θ$ with the horizontal, this new velocity must make an angle $90^{\circ} - θ$ with the horizontal.
Throughout the motion, only external force acting is gravitational in the vertical direction. Thus the horizontal velocity remains the same.
Thus $u c o s θ = v s i n θ$
$⟹ v = u c o t θ$

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A particle is projected with a velocity u making anangle θ with the horizontal. At any instant, its velocity v is at right angles to its initial velocity u; then v is:

A particle is projected with a velocity $u$ making anangle $θ$ with the horizontal. At any instant, its velocity $v$ is at right angles to its initial velocity $u$ ; then $v$ is: