A particle slides down a smooth incline of inclination `37^(@)`, fixed in an elevator going up with an acceleration `(g)//3`. The base of incline has a length `5m`. Find the time taken by the particle to reach the bottom.

Explanation

If we work from reference frame attached to an elevator (an accelerated frame), we have to apply a pseudo force `ma_(0)` on the block.

`a:` acceleration of w.r.t. incline along the plane`:`
`m((g+a_(0))sintheta=ma`
`a=(g+a_(0))sintheta=(g+(g)/(3))sin37^(@)`
`(4g)/(3).(3)/(5)=8m//s^(2)`
The distance trabveled by the particle from the top to the bottom.
`a(5)/(cos37^(@))=(5)/(4//5)=(25)/(4)m`
`d=(1)/(2)at^(2)rArr(25)/(4)=(1)/(2)xxsxxt(2)rArrt=(5)/(4)s`