question_answer 54)

  Two stones are thrown vertically upwards simultaneously with their initial velocities  and  respectively. Prove that the height reached by them would be in the ratio of  (assume upward acceleration is ? g and downward acceleration to be + g).  

Answer:

  For 1st stone, given initial velocity Let height attained by it be . From third equation of motion, for upward motion [Here, we have used negative sign, because as given upward acceleration is taken to be ?q At the highest point the velocity becomes zero i.e., v = 0                           Similarly, For 2nd stone, given initial velocity, Let the height attained by it be . From third equation of motion, [at the highest point the velocity becomes zero i.e., v = 0]                                                                      Now, ratio of heights reached by the two stones                                         Hence proved