At `t=0` a projectile is fired from a point `O` (taken as origin) on the ground wita speed of `50m//s` at an angle of `53^(@)` with the horizontal. It just passes two points `A` and `B` each at height `75m` above horizontal.

The horizontal separation between the points `A` and `B`

Options

A. 30 m
B. 60 m
C. 90 m
D. None

Answer

D

Explanation

`v_(1)sintheta_(1)=v_(2)sintheta_(2)`
Time of flight `T=(2xsintheta)/(g)`
`T_(1)=(2v_(1)sintheta_(1))/(g)=(2v_(2)sintheta_(2))/(g)=T_(2)`
Maximum height `H_("max")=(x^(2)sin^(2)theta)/(2g)=((xsintheta))/(2g)`
`H_("max")=((v_(1)sintheta_(1))^(2))/(2g)=((v_(2)sintheta_(2)))/(2g)=H_("2max")`
`vec(a)_("rel")=-ghat(j)+ghat(j)=0`
`because vec(a)_("rel")=0` & time of flight is same the trajectory of one w.r.t. other is a straight line.