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A particle is projected with a velocity ...

A particle is projected with a velocity (u) so that its horizontal range is thrice the greatest heitht attained. What is its horizontal range?

A

`(u^(2))/(5g)`

B

`(2u^(2))/(5g)`

C

`(3u^(2))/(5g)`

D

`(4u^(2))/(5g)`

Text Solution

Verified by Experts

Greatest height attained `h=(u^(2) sin^(2) 0)/(2g)…….(1)`
Horizontal range `R=(u^(2) sin20)/(g) =(2u^(2) sin 0 cos 0)/(g) ……(2)`
Given that R=2h
`rarr (2u^(2) sin 0 cos 0)/(g) =(2u^(2) sin^(2)0)/(2g) rarr tan 0=2" …….(3)`
Hence `sin 0=2//sqrt(5), cos 0=1//sqrt(5)`,
From (2) `R=4u^(2)//5g`
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