Messages posted by lakshmiaswin

a 45 kg skater moving at 10 m/s is picked up by her 7 5kg partner who is skating in the same direction at 18m/s. They move of together. What is th evelocity of the centre of mass before he picks her up and after

it's d)9g/4

Accdg to relation g=GM/R^2 , where R is radius of Earth

1) First find the pts on the line: x= 3K-2, y= 4k-3/2, z= 5k+4/32)then find the dr's of the line joining x.y,z and (-2, 3, -4)3)the normal to the plane and the line are perpendicular.4)find k5)get pt on line and find dist using dist fml

cos?x+ cos?y+ cos?z =∏

cos?x+ cos?y = ∏ - cos?z

= cos? (-z)

cos?( xy- √ (1-x^s)√(1-x^2)) = cos? (-z)

xy- √ (1-x^s)√(1-x^2)) = -z

√ (1-x^s)√(1-x^2) = xy+z

Then square

(Sinx)^1/2
Let sinx=t^2
Cosx dx=2t dt
Sub
Thus eqn becomes
2t^2dt/cosx , but cos x =1-t^4
Eqn is 2t^2 dt/1-t^4
= (t^2+1/1-t^4)+ (t^2-1/1-t^4)
={t^2+1/(1-t^2)* (1+t^2)}+ {t^2-1/(1-t^2)* (1+t^2)}
= integral (1/1-t^2)- integral(1/1+t^2)
= ½ ln{1+t/1-t} - tan?1 1/t
Re substitute t as sinx

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