It is possible to project a particle with a given velocityin two possible ways so as to make them pess through a point P at a horizontal distance r from the point of projection. If `t_(1)` and `t_(2)` are times taken to reach this point in two possible ways, then the product `t_(1)t_(2)` is proportional to

Options

A. (a) `1/(r)`
B. (b) r
C. (c ) `r^(2)`
D. (d) `1/(r^(2))`

Answer

(b)

Explanation

Time of flight, `t_(1) = 2Usintheta/(g)`
`t_(2) = 2Ucostheta/(g)`
`t_(1)t_(2) = 4U^(2)sin(theta)cos(theta)/(g^(2)) = 2r/(g)`
`:. t_(1)t_(2) alpha r`