# a particle of mass m is projected with a velocity v making an angle of 45 degrees with the horizontal. the magnitude of the angular momentum of the projectile about the point pf projection when the particle is at its max height

420 Points
13 years ago

Dear Pranay

max height ,H= v2sin2θ/2g

velocity at max height = ux= vcosθ

angular momentum= muxH

and putting θ =450

angular momentum = mv3/g4√2

All the best.

AKASH GOYAL

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509 Points
13 years ago

if the point of projection is taken as origen then

coordinates of maximum height (H,R/2)       or r =Hi + (R/2)j       in vector  form

R is horizontal  range  and H is maximum height ....

at maximum height there is only horizontal component of velocity no vertical component exists ...

so , V= vcos@i  ......

linear momentam = mvcos@i                     ( @ is the angle of projection)

we know that angular momentam(L) about point of projection = r*p                (* is cross product)

L  =(Hi + (R/2)j)*(vi)

L  =Rv/2 (-K)

L=v3 /2g (-k)                                       ( R =v2 /g at @=45 degree)