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The velocity of projection of a particle if it does not rise more than 3m in a range of 600m will be _

The velocity of projection of a particle if it does not rise more than 3m in a range of 600m will be _

Grade:12th pass

1 Answers

Arun
25763 Points
2 years ago

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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