Projectile motion homework help

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Discussion Overview

The discussion revolves around the application of gravity in projectile motion, specifically addressing why gravity is consistently treated as a negative value (-9.8 m/s²) when calculating the time of flight for a projectile, despite the differing motion during ascent and descent.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about why gravity is treated as negative throughout the projectile's flight, suggesting that it only seems negative during the ascent.
  • Another participant explains that the negative sign is a convention indicating direction, with positive values representing upward motion and negative values representing downward motion.
  • A different participant references Newton's second law, emphasizing that the gravitational force always points downwards, which aligns with the negative coordinate system used in calculations.
  • One participant argues that during the ascent, the object is decelerating, while during descent, it is accelerating, questioning the consistency of using -9.81 m/s² for both phases in calculations.
  • Another participant reiterates that the acceleration due to gravity remains directed downwards, and the negative sign does not imply deceleration but rather indicates direction.
  • A participant introduces an equation for calculating time of flight and questions whether the displacement should be considered positive or negative based on the maximum height.
  • One participant expresses gratitude for the clarification received, indicating a better understanding of the topic.
  • Another participant reinforces the idea that the sign of acceleration indicates direction rather than deceleration or acceleration in the conventional sense.

Areas of Agreement / Disagreement

Participants exhibit a mix of understanding and confusion regarding the treatment of gravity in projectile motion calculations. While some agree on the convention of using negative values for downward acceleration, others question the implications of this convention during different phases of motion. The discussion remains unresolved regarding the nuances of how to interpret the signs in various contexts.

Contextual Notes

Participants express uncertainty about the implications of using negative acceleration during different phases of projectile motion, highlighting potential confusion regarding the relationship between direction, acceleration, and deceleration.

nirvana1990
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Why is gravity always taken as negaive when applied to the whole projectile i.e. when finding the time of flight for the entire projectile we use gravity as -9.8 even though it is only negative for the first half of the projectile while the object is moving upwards against gravity?
Please help as i am very confused!

:rolleyes:
 
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Its just a convention. Positive speed and positive acceleration tell us that it is directed upwards whereas negative speed and negative acceleration indicate a downward motion. it would work just as well the other way around if a little counter intuitive.
 
Welcome to PF!

nirvana1990 said:
when finding the time of flight for the entire projectile we use gravity as -9.8 even though it is only negative for the first half of the projectile while the object is moving upwards against gravity?

I'm not sure what you mean by that.

Remember Newton's second law? It says that direction of the force and acceleration are the same. At all times during the motion of the projectile the direction of the force of gravity (we assume a uniform gravitational field) always points down, towards the ground. Also, for convenience, we usually set up the coordinate system such that the negative y-axis points in this direction. Therefore the gravitational force, [itex]F_g = -mg\hat{y}[/itex].
 
Right...but since gravity always acts downwards, the acceleration for the 1st half of the projectile motion should be -9.81 since the object is decelerating towards its max. height but the acceleration for the downwards projectile motion (e.g.when the ball is on it's way back down to earth) should be +9.81 since the ball is accelerating. So when calculating the time of flight using S=Ut+0.5at^2 applied to the vertical motion only why do we use a as -9.81 even though a should only be negative while the ball is going upwards?
I hope this is understandable! i have a way with words!
 
The acceleration is always downwards. In the coordinate system that is conventional downwards is represented by a negative sign. The sign doesn't change once the projectile starts falling to Earth.

I think you are confusing a negative sign to mean deceleration and a positive to mean acceleration and that is just not the case. The sign indicates the direction of the acceleration.
 
nirvana1990 said:
So when calculating the time of flight using S=Ut+0.5at^2 applied to the vertical motion only why do we use a as -9.81 even though a should only be negative while the ball is going upwards?

For a body accelerating towards the ground, the equation would actually read,

[tex]s = h_{max} + ut + \frac{1}{2}at^2[/tex]

u = 0, therefore [itex]s - h_{max} = \frac{1}{2}at^2[/itex]. Is [itex]s - h_{max}[/itex] positive or negative?
 
Last edited:
Oh i see, i'd never have thought of it like that! Thank you soo much! I can now rest!
 
Kurdt said:
I think you are confusing a negative sign to mean deceleration and a positive to mean acceleration and that is just not the case. The sign indicates the direction of the acceleration.

That's true. When the direction of the velocity and acceleration are opposite, then the body is slowing down, or decelerating.
 

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