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Max. Height = 3m = u2Sin2theta / 2g
.
u2Sin2theta / 2g = 3
u2Sin2theta = 60
uSintheta = root60
u =root60 /Sintheta .......... 1
Range = 600m = u2Sin2theta / g
u2Sin2theta / g = 600
u2Sin2theta = 6000
Replacing u from 1:-
(60 / Sin2theta) (Sin2theta) = 6000
(1 / Sin2theta) (2.Sintheta.Costheta) = 6000 / 60 = 100
2Costheta / Sintheta = 100
Cot theta = 100/2 = 50
Theta = Cot inv of (50) = 1 degree,
Therefore Sin 1 = 0.0209
Replacing sin in 1:-
u =root60 /Sintheta
u = 7.74 / 0.0209 = 370 m/s
Hence velocity of projection = 370 m/s
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