Pankaj and Sudhir are playing with two different balls of masses m and 2m, respectively. If Pankaj throws his ball vertically up and Sudhir at an angle θ with the verticle, both of them stayin our view for the same period. The height attained by the two balls are in the ratio

Time of flight for the ball thrown by Pankaj, T1=2u1gTime of flight for the ball thrown by SudhirT2=2u2 sin⁡90∘−θg=2u2 cos⁡θgAccording to problem T1=T2⇒2u1g=2u2cos⁡θg⇒u1=u2cos⁡θHeight of the ball thrown by pankaj H1=u122gHeight of the ball thrown by SudhirH2=u22sin2⁡90∘−θ2g=u22cos2⁡θ2g∴ H1H2=u12/2gu22cos2⁡θ/2g=1                As u1=u2cos⁡θ