If a 100 ~m long train needs 7.2 ~s to cross an object moving in a direction opposite to the train's direction with a speed of 5 ~km / h , then find the velocity of the train.

Step-by-step solution

Given, length of train, l=100 ~m Time taken by an object to cross the train, t=7.2 ~s Velocity of object opposite to train, v₀=5 ~km ~h ⁻¹ aligned & = 25 18 ~m / s & =1.39 ~m / s aligned Let the velocity of train, v_t=v Using the concept of relative motion. Relative velocity of train w.r.t object v_ rel =v_t+v₀ Now, l=v_ rel t100=7.2 (v_t+v₀ ) 100=7.2(v+1.39) v=12.5 ~m / s =45 ~km ~h ⁻¹