circular motion

SUM 1:::
a particle is projected at a speed u at anangle thita{-}
wid the horizonatal
consider a small part near the highest position and take it to b a approx circular arc
Wht is d radius of this circle....????this radius is called the radius of curvature at this point

.
SUM 2
:::
wht is the radius of curvature of the parabola
traced
out by d projectile in d previoous problem
at a point where the particle
velocity
makes an angle [thita/2]
wid the horizontal

plz explain the second problem while solving...

2 Answers

1
satan92 ·

for sum 1
we have
mv2/R=mg

but v= ucosθ

hence R=u2cos2θ/g

1
satan92 ·

for sum 2

let the velocity of object be v

then vcosθ/2=ucosθ(as horizontal component does not change)

hence we get v

and acceleration of particle perpendicular to velocity =gcosθ/2

so

v2/R=gcosθ/2

hence R=u2cos2θ/gcos3θ/2

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