For a given angle of projection, if the time of flight of a projectile is doubled, the horizontal range will increase to :

Options

A. four times
B. thrice
C. once
D. twice

Answer

A

Explanation

Here `R=(u^(2)sin2theta)/g` and `T=(2usintheta)/g`
Now `T^(2)=(4u^(2)sin^(2)theta)/(g^(2))=(2(2u^(2)sintheta.sintheta)/g^(2))`
`g t^(2)=(2u^(2)sin2theta)/g.tantheta`
`g t^(2)=Rtantheta`
As .g. and tan`theta` are constants R `prop T^(2)`
When .T. is doubled .R. becomes 4 times.