Calculating relative distance covered Two balls 'A' and 'B' are thrown vertically upwards with the same velocity. The mass of A is greater than that of B. We need to find which of the balls reaches a greater height (assuming the effect of air resistence is negligible).
I personally feel that A would travel further since its momentum is higher than that of B. But few people whom I discussed this question with had different opinion. 
One said that they would both travel the same distance since $s=(ut) + (1/2)at^2$
The other said that B would travel further since the effect of gravity on it is less according the universal law of gravitation.
If someone could explain which of these is correct or maybe point out the flaw in either of them then it would help a lot. Thanks in advance.
 A: If the mass of an object is $m$ then its weight is $mg$ where $g$ is the gravitational field strength.
Assuming that no other forces act on the mass and apply Newton's second law 
$F = ma \Rightarrow mg = ma \Rightarrow a = g$ 
where $a$ is the acceleration of the mass shows that the acceleration of a mass is independent of its mass.
So as your two masses had identical initial conditions and undergo the same acceleration then their motions must be the same.
A: Effect of gravity does not depend on the mass of the balls. If you draw free body diagram each of these objects, you will see that masses are cancel each other. So, both of them has the same distance after they are thrown vertically. Greetings :)
A: Your question stems from not knowing the difference between kinematics and dynamics. This link will help you What is the difference between "kinematics" and "dynamics"? to ask relevant questions
A: If the objects have same initial velocity, they should travel the same distance. Momentum has no picture there.
But when they reach the peak height, they stop for a fraction of second (or lesser), that's where your mass comes into picture as their potential energies come into picture. 
Momentum comes into picture when they come in contact with another object, or the ground. The heavier object would make a bigger (or deeper) impact on the ground (impact surface) than the lighter one. But as for travelling distance and velocity of travel, it should be the same as the equations are (clearly) mass independent. 
A: the thing you have missed to mention is effect of air resistance.If we include the effect of air resistance in this question then role of mass will come into play, but if you are not including air resistance then you will use s=ut+at^2/2, which is independent of mass so both bodies will traverse the same distance.Hope my message reach you. 
