A car can pull a trailer of twice its mass up a certain slope at a maximum speed `v=1m//s`. Without the trailer the maximum speed of the car up the same slope is `2v`. The resistance to the motion is proportinal to mass and square of speed. If the car (without trailer) starts to move down the same slope, with its engine shut off, eventually it will acquire a constant speed `v_(t)`, then find `v_(t)^(2)` (in `m^(2)//s^(2)`)

Answer

5

Explanation

For car `+` trailer system
`P_("max")=(3mgsintheta+3kmv^(2))v`
For car only
`P_("max")=(mgsintheta+4kmv^(2))2v`
`:.k=(gsintheta)/(5v^(2))`
For down the incline `kmv_(t)^(2)=mgsintheta`
`:.v_(t)^(2)=5v^(2)`