- #1
Curiosity_0
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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?
B Time for which a vertical projectile stays motionless in midair
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When a projectile is thrown vertically, it momentarily stops at its highest point, but this stop occurs instantaneously, lasting zero seconds. The velocity at this peak is zero only at that exact moment, as it transitions from positive to negative velocity due to gravity. The acceleration is a constant negative value, leading to a linear decrease in velocity until it reaches the ground. Understanding this concept requires the application of Differential Calculus, which allows for the calculation of instantaneous values as intervals approach zero. Thus, while the projectile appears to stop, it does so without any measurable duration.
- #2
Baluncore
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That moment will be an instant, not a period of time.
- #3
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It's zero seconds. It's the same for any other velocity on its trajectory.Curiosity_0 said:
- #4
berkeman
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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?Curiosity_0 said:
https://cnx.org/resources/d7690f6d7871dafd158630fc8ea5b60846d9c9bf/PG12C1_007.png
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- #5
Herman Trivilino
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It will stop at a particular clock-reading, but that clock-reading lasts for zero time.Curiosity_0 said:
As soon as the projectile reaches its highest point it starts to descend, it spends zero time at the highest point
- #6
sophiecentaur
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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.Curiosity_0 said: