A particle slides down on a smooth incline of inclination 30^ , fixed in an elevator going up with an acceleration 2 ~m / s ^2 . The box of incline has a length 4 m . The time taken by the particle to reach the bottom will be

Step-by-step solution

In the frame of elevator, a= acceleration of the particle with respect to the elevator aligned m 30(g+2) & =m a a & =(g+2) 30^ & =(10+2) 1 2 & =6 ~m / s ^2 aligned The distance travelled by the particle from the top to the bottom, aligned d & = 4 30^ = 4 3 / 2 = 8 3 3 ~m Using s & =u t+ 1 2 a t^2, aligned aligned & & 8 3 3 & =0 t+ 1 2 6 t^2 & & t^2 & = 16 3 3 6 & & t & = 4 3 3 2 ~s aligned