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With what minimum speed must a particle ...

With what minimum speed must a particle be projected from origin so that it is able to pass through a given point `(30m, 40m)` ? Take `g=10m//s^(2)`

A

60 m/s

B

30 m/s

C

50 m/s

D

40 m/s

Text Solution

Verified by Experts

The correct Answer is:
B

`30=u cos theta t`
`40=u sin theta t-(10t^(2))/(2)`
`rArr 40=30 tan theta -(5(30))/(u^(2) cos^(2) theta)`
`rArr 450 tan^(2) theta-3u^(2) tan theta+450+4u^(2)=0`
`rArr 9u^(4)-1800(450+4u^(2)) ge 0`
. `rArr u^(4)-900u^(2)+100u^(2)-90,000 ge 0`
`rArr u^(2)=-100 or 900 rArr u=30m//s`
`rArr 4=3 tan theta-(450)/(u^(2))(1+tan^(2) theta) tan theta" is real "rArr D ge 0`
`rArr u^(4)-800u^(2)-90,000 ge 0`
`rArr u^(2) (u^(2)-900)+100 (u^(2)-900 ge 0`
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