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A particle is projected with velocity 20...

A particle is projected with velocity `20sqrt(2)m//s` at `45^(@)` with horizontal. After `1s` , find tangential and normal acceleration of the particle. Also, find radius of curveture of the trajectory at that point. (Take `g=10m//s^(2))`

Text Solution

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The correct Answer is:
A, B, D
After `1s` , `v=u+at=20hat(i)+10hat(j)` ,
`v=sqrt(500)m//s=10sqrt(5)m//s`
`a=-10hat(j)`
`a_(t)=acostheta`
`=(a.v)/(v)=(-100)/(10sqrt(5))`
`=-2sqrt(5)m//s`
`a_(n)=sqrt(a^(2)-a_(t)^(2))=sqrt((10)^(2)-(2sqrt(5)^(3)))`
`=sqrt(80)m//s^(2)=4sqrt(5)m//s^(2)`
`R=(v^(2))/(a_(n))= (10sqrt((5)^(2)))/(4sqrt(5))=25sqrt(5)m` .
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