Question

A body is projected with velocity u making an angle theta with the horizontal. Its velocity when it is perpendicular to the initial velocity vector is

Answer 1

Projectile is an object projected with some velocity and its initial direction of motion makes an angle α ( α >0 and α <90°) with horizontal direction. Projetile moves in a …

Answer 2

hey mate here is your answer

A projectile moves with speed u and inclined with horizontal is ∅

then, initial velocity vector (U)

= ucos∅i + usin∅ j

let at time = t velocity of projectile is perpendicular upon initial velocity .

then, that time velocity ( V)= ucos∅ i + ( usin∅ -gt) j

now,

U and V are perpendicular so,

dot product of U and V = 0

( ucos∅ i + usin∅ j ){ucos∅i +( usin∅-gt)j } = 0

u² cos²∅ + u²sin²∅ -usin∅gt = 0

u²( cos²∅ + sin²∅ ) = usin∅gt

u = sin∅ gt

t = u/gsin∅

now , put this in V

V = ucos∅i + ( usin∅ -gu/gsin∅)j

= u cos∅i + u( sin²∅ -1)/sin∅ j

= ucos∅i - ucos²∅/sin∅ j

magnitude of V

V = u √( cos²∅ + cos²∅cot²∅)

u√( cos²∅(1 + cot²∅))

=u√cos²∅(cosec²∅)

=ucot∅

hence , V = ucot∅

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