Velocity Question: Initial vs. Final Velocity at y=0

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In projectile motion, the final velocity (Vf) at y = 0 is equal in magnitude to the initial velocity (V0) but opposite in direction, assuming no air resistance. This means that while the speeds are equal, the velocities differ due to their directions. If external forces like air resistance are considered, Vf will be less than V0. The conservation of energy principle supports this, as the kinetic and potential energy balance leads to the conclusion that |V0| = |Vf| when the object reaches the ground. Thus, the final velocity is not zero but rather equal in magnitude to the initial velocity just before impact.
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My question is... If I have an initial velocity (V0) will the final velocity(Vf) at y = 0 be equal?

I created a diagram if the question is confusing...
If so, why is this true? Because wouldn't final velocity be zero??
 

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Essentially these types of problems are asking you the velocity at the instant before the object collides with the ground. Hence, unless there are external forces dissipating the objects energy, its final (at the instant before it touches ground) will equal its initial.
 
I think this is the qoestion on projectile motion. If air resisance is neglected, final velocity is equal to initial velocity. It will never become zero throughout the time of flight. if air resistance is included, final velocity will be less than initial one.
 
Miike012 said:
My question is... If I have an initial velocity (V0) will the final velocity(Vf) at y = 0 be equal?

I created a diagram if the question is confusing...
If so, why is this true? Because wouldn't final velocity be zero??

The velocities in the picture are not equal, but of equal magnitude, as the directions differ. You can say that the speeds are equal.

If it is a projectile, the horizontal component is constant during the motion as only vertical force -gravity- acts on the object. Energy is conserved, so mgyi+1/2 mvi2=mgyf+1/2 mvf2. If yi=yf the square of the velocities are equal, vi2=vf2. That means equal magnitudes |vi|=|vf|, that is, equal speeds.


ehild
 
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