Rate of decrease in distance between two objects moving with certain speed towards each other is 6 m/s and rate of decrease decrease in distance between those objects with same speed when move in some direction is 4 m/s. Then the speeds of objects are .......

Options

A. `5 m//s, 1m//s`
B. `4m//s, 2 m//s`
C. `4m//s, 1m//s`
D. `5 m//s, 2 m//s`

Answer

A

Explanation

Suppose speed of object 1 is `v_(1)` and that of object 2 is `v_(2),` also `v _(1) gt v _(2).`
If v is relative speed when they re moving in same direction, then
`v = v _(1) + v _(2) `
`therefore 6= v _(1) + v _(2) " "…(1)`
If v. is relative speed when they are moving in same direction, then
`v. = v _(1) -v _(2)`
`therefore 4= v _(1) -v _(2) " "...(2)`
By adding equation (1) & (2),
`10 = 2v _(1) implies v _(1) = 5m//s`
From equation (2),
`v _(1) = 5m//s`