A transparent lift A is going upwards with velocity 20 ~ms ⁻¹ and retarding at the rate of 8 ~ms ⁻² . Second transparent lift B is located in front of it and is going down at 10 ~ms ⁻¹ with retardation of 2 ~ms ⁻² . At the same instant a bolt from the ceiling of lift A drops inside lift A. If height of car of lift A is 16 m then find the distance travelled by bolt as observed by a person in lift B till the time it co

Step-by-step solution

In the ref. frame of A : array ll V _ b / A =0 & a _ b / A =2 ~m / s ^2 ~S _ b / A =16 ~m - & T = ( 2 16 2 ) =4 ~s & for Bolt (b) : t ₁= 30 12 = 10 4 =2.5 ~s & 0=30-12 ( t ₁ ) h ₁= 75 2 & ~h ₁= (30)^2 2(12) = 900 24 array In the ref. frame of B : array lll V _ b / B =30 ~m / s - & a _ b / B =12 ~m / s ^2 & ~T =4 ~s ~V _ A / B =30 ~m / s - & a _ A / B =10 ~m / s ^2 & array for A : S _ A / B =30(4)- 1 2 (10)(4)^2=120-80=40 distance =2 ~h ₁+ h - S _ A / B =75+16-40=51 ~m