Question

A body of mass m is thrown from a building of height h in upward direction and reach maximum height x . From height x its start falling down. calculate the ratio of velocity of body at height h and just before reaching the ground​

Answer 1

Step 1: Time taken to reach the maximum height (t1)    [Ref. Fig.]

At maximum height V=0 

Since acceleration is constant, therefore applying equation of motion in y direction. Taking upward positive

             V=u+at1                 [a=−g m/s2]

⇒         0=u−gt1

⇒           t1=gu                                                                         ....(1)

Step 2: Time taken to hit the ground (t2)

 Applying the 2nd equation of motion

              s=ut2+21at22           [s=−H]

⇒       −H=ut2−21gt22                                                  ....(2)

Given that t2=nt1=gnu                                                      ....(3) 

Step 3: Solving above equations

Substitute the value of t2 from  (3)  in (2)

             −H=u×gnu−