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A particle is projected at time t=0 from...

A particle is projected at time t=0 from a point P wilth a speed `v_0` at an angle of `45^@` to the horizontal. Find the magnitude and the direction of the angular momentum of the particle about the point P at time `t=v_0/g`

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Velocityat time .t. is `barv=v_(x)bari+v_(y)barj`
position vector of projectile at time .t. is `barr=xbari+ybarj` since `barL=m(barrxxbarv)`
`barL=m[(xbari+ybarj)xx(v_(x)bari+v_(y)barj)]`
`barL=m[xv_(y)bark-yv_(x)bark]`
`impliesbarL=mbark[xv_(y)-yv_(x)]`
where `v_(x)-(u)/(sqrt(2))` and `x=(u^(2))/(sqrt(2)g)`
`v_(y)=usin45-"gt"=(1-sqrt(2))/(sqrt(2)).v_(0)`
`y=usin45.t-(1)/(2)"gt"^(2)=(y^(2))/(2g)(sqrt(2)-1)`
`:.barL=-bark^(mu^(3))//2sqrt(2)g`
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