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Q.

A body is thrown with the velocity vo at an angle of θ to the horizon. Determine vo in ms-1 if the maximum height attained by the body is 5 m and at the highest point of its trajectory the radius of curvature is r = 3 m. Neglect air resistance.  [Use 80 = 9 and g =10 m/s2]

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answer is 9.

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Detailed Solution

Radius of curvature at the highest pointmv2r=mg r=v2g⇒r=v0cos⁡θ2gv0cos⁡θ=gr              ……… (i)Maximum height, h=v02sin2⁡θg⇒v0sin⁡θ=gh           ………. (ii)By using Eqs (i) and (ii), we getv02sin2⁡θ+v02cos2⁡θ=gh+gr=g(h+r)⇒ v0=g(h+r)=10(5+3)=9ms−1
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