Two balls A and B are projected from the same position with horizontal velocity `20 ms^(-1)` and `5 ms^(-1)` as shown. The separation between these two bodies at the moment their velocities become perpendicular to each other is x m. The value of x is

Answer

25

Explanation

`vecv_(1) = 5hati - "gt"hatj rArr u_(1) = 5`
`vecv_(2) = 20hati - "gt"hatj rArr u_(2) = 20`
As `vecv_(1)` and `vecv_(2)` are perpendicular,
`vecv_(1).vecv_(2) = 0`
`t = sqrt(u_(1).u_(2))/g`
`vecs_("rel") = vecu_("rel") xx t`
` = (u_(1) + u_(2))t`
`= (u_(1) + u_(2))sqrt(u_(1).u_(2))/g`
` = 25 xx 10/10 = 25 m`