# Question related to Mechanics of rigid bodies  Why the initial momentum at the highest point became zero. why it can't be sum of those two Vertical components.

At the highest point, we have $$v_x = v sin \alpha$$ and $$v_y = 0$$ for each particle, although their $$v_x$$ are in opposite direction. [$$v_y$$ = 0 at the top of a projectile]

Hence, $$p_y = 0$$ and $$p_x = m v_x + m (-v_x) = 0$$. So momentum is $$0$$ at the top and combined particle falls vertically downwards.

Hope it helps.

• Hi, Thanks for your explanation. You mentioned that the vertical component of velocity at highest point is zero. The term usin(a) is zero right. That means either u = 0 or angle a = 0. Cause we are taking about initial momentum, the initial velocity u is not zero and the angle a is also not zero. Then how the vertical component became zero when we are talking about initial momentum.
– Sai
Jun 1, 2022 at 7:00
• @Sai I just saw your comment now, apply v = u + at in the y direction, where u = u sin alpha and a = -g, t = u sin alpha / t, hence v = 0 in the y direction. See some reference about projectile motion in general form, en.m.wikipedia.org/wiki/Projectile_motion. Jun 1, 2022 at 9:06
• And if you don’t mind could you please select my answer as I answer earlier. Jun 1, 2022 at 9:06
• Thanks @Sai for selecting my answer ! Jun 2, 2022 at 3:28

See, at highest point point the vertical component of velocity is zero, and we are having only horizontal velocity of these 2 masses, whose magnitude is ucos(a) , where 'a' stand for alpha. in y-direction,

velocity of both masses is zero, so momentum =0 in x- direction, one is having the velocity towards left and one towards right, and momentum is a vector quantity having direction in direction of velocity of body, so if one velocity is taken positive , other will be negative, so adding them will again give us zero.

• Hi, Thanks for your explanation. You mentioned that the vertical component of velocity at highest point is zero. The term usin(a) is zero right. That means either u = 0 or angle a = 0. Cause we are taking about initial momentum, the initial velocity u is not zero and the angle a is also not zero. Then how the vertical component became zero when we are talking about initial momentum.
– Sai
Jun 1, 2022 at 7:00
• see friend, usin(a) is the initial vertical component of velocity, it is not velocity at highest point , i got what you are thinking , you are conserving momentum initially when these are projected and finally when they are at highest point , but this can't be done because there is force of gravity in vertical direction , although you can conserve momentum between these points in horizontal direction as there is no force. we are conserving momentum just before and just after collision and that too on the system of the two masses, not on individuals as there is impulsive force due to collision. Jun 1, 2022 at 7:19
• In that case can we assume that vertical component of velocity is balanced by the gravitational force at the highest point. I'm just trying visualize the scenario in my mind.
– Sai
Jun 1, 2022 at 8:07
• no, only those things can be balanced which have same units. here mass rises up, and gravity applies force in opposite direction and retards the motion ,and finally velocity becomes zero we call it highest point , because after that it starts moving downwards due to gravity . Jun 1, 2022 at 8:29
• Thank you bro for explaining
– Sai
Jun 1, 2022 at 8:52