Time for which a vertical projectile stays motionless in midair

[Curiosity_0]

We know that if a projectile is thrown vertically, there will be a brief time when it momentarily stops. Can we calculate this brief moment?

 

[Baluncore]

That moment will be an instant, not a period of time.

 

[PeroK]

We know that if a projectile is thrown vertically, there will be a brief time when it momentarily stops. Can we calculate this brief moment?

It's zero seconds. It's the same for any other velocity on its trajectory.

 

[berkeman]

We know that if a projectile is thrown vertically, there will be a brief time when it momentarily stops. Can we calculate this brief moment?

As others have said, the velocity is zero only instantaneously. These plots of the vertical motion of a projectile should help. See how the acceleration due to gravity is a constant negative value (-g)?, and how the velocity decreases linearly from the initial $v_0$ down through zero to end up being $-v_0$ when the projectile impacts the ground?

https://cnx.org/resources/d7690f6d7871dafd158630fc8ea5b60846d9c9bf/PG12C1_007.png

 

[Mister T]

We know that if a projectile is thrown vertically, there will be a brief time when it momentarily stops. Can we calculate this brief moment?

It will stop at a particular clock-reading, but that clock-reading lasts for zero time.

As soon as the projectile reaches its highest point it starts to descend, it spends zero time at the highest point

 

[sophiecentaur]

We know that if a projectile is thrown vertically, there will be a brief time when it momentarily stops. Can we calculate this brief moment?

We 'think' we know that. Reasonable enough because things happen pretty slowly at the high point it would really boil down to how quickly and accurately we could actually measure that velocity. Zero velocity is actually no more special than +1m/s or -1.05m/s. This was a problem for the old Physicists until the concepts involved in Differential Calculus were introduced. The theory is that you consider a smaller and smaller interval between two (imagined) measurements the limit as the interval approaches zero is the 'true' value of the velocity.