The distance between two trucks moving towards each other is decreasing at the rate of 10m/s. If these trucks travel with same speeds in same direction the separation increases at the rate of 5m/s. The speeds of the trucks are :

Options

A. `V_(1)=8.5m//s,V_(2)=1.5m//s`
B. `V_(1)=7.5m//s,V_(2)=2.5m//s`
C. `V_(1)=5m//s,V_(2)=5m//s`
D. None of these

Answer

B

Explanation

According to the given equation First case: Separation between the trucks decreases at the rate of 10m/s. Due to the opposite relative motion of trucks away from each other-
`V_(1)+V_(2)=10` (condition given) . . .(1)
Seconds case: Separation between the trucks increases due to the opposite relative motion of trucks away from
each other-
`V_(1)-V_(2)=5` . . . (2) (condition given)
From equation (1) and (2), we get
`V_(1)+V_(2)=10` . . .(i)
`V_(1)-V_(2)=5` . . (ii)
`Eq^(n)(i)+(ii)`
`2V_(1)=15`
`V_(1)=7.5m//s`
Eqn(i)-(ii)
`2V_(2)=5`
`V_(2)=2.5m//s`