A car going at a speed of 6m/s when it encounters a 15m slope of angle `30^(@)`. The friction coefficient between the road an tyre is 0.5. the driver applies the brakes. The minimum speed of car with with which it can reach the bottom is `(g=10m//s^(2))`

Options

A. `4 m//s`
B. `3 m//s`
C. `7.5 m//s`
D. `8.45 m//s`

Answer

C

Explanation

`a=ug cos 30^(@)-gsin 30^(@)`
`=0.5xx10xx(sqrt3)/(2)-(10)/(2)=-0.675m//s^(2)`
`rArr a=0.675m//s^(2)` is downward direction
`rArr v^(2)=u^(2)+2as=36+2xx0.675xx15`
`v^(2)=56.25rArr v=7.5m//s`
`mu=(1)/(sqrt3)=0.577~~0.6`