If object A is half the mass of object B, then is it possible for them to have the same momentum
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It depends on both of them.
In fact, the projectile begins its motion with an initial velocity of
and an angle of 
. On the y-axis (vertical direction), it is an accelerated motion with acceleration equal to -g (gravitational acceleration). The vertical velocity of the projectile at any time t is given by
and as it can be seen, this depends on both initial velocity and angle.
In fact, the projectile begins its motion with an initial velocity of
and as it can be seen, this depends on both initial velocity and angle.