Mistake in Physics textbook equation

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Discussion Overview

The discussion revolves around a potential mistake in a physics textbook regarding the equations for the vertical component of velocity in projectile motion. Participants explore the implications of different interpretations of the angle and the correct application of kinematic equations.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions the correctness of the textbook formula for the final velocity in the y direction, suggesting an alternative equation yields correct answers.
  • Another participant argues that the correctness of the formula depends on how the angle is defined, indicating that sine or cosine may be appropriate based on the angle's reference.
  • A different participant provides context, suggesting the formula is for the vertical component of velocity for an object thrown at an angle θ with respect to the horizontal, asserting the textbook's formula is correct.
  • One participant supports the textbook's correctness by referencing kinematic equations, noting the distinction between velocity and displacement in their application.
  • Another participant reiterates the textbook's equation for altitude and attempts to derive the velocity equation, but is challenged on their reasoning regarding the derivative.
  • One participant mentions that angles are typically measured with respect to the horizontal in these problems, except in specific contexts like aviation.
  • A participant acknowledges the derivative concept but notes a lack of calculus knowledge in their course, indicating a gap in understanding the reasoning behind the equations.

Areas of Agreement / Disagreement

Participants express differing views on the correctness of the textbook's formula and the interpretation of the angle. There is no consensus on whether the formula is a misprint or if it is contextually correct based on angle definitions.

Contextual Notes

Participants highlight the importance of angle definitions and the application of kinematic equations, but there are unresolved assumptions regarding the context of the problem and the mathematical steps involved in deriving the equations.

goochmawn314
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There is a formula in my textbook and I have a strong feeling it's incorrect.

The formula the book says is

velocity in y direction (final) = (vi)(sinx) - gt

Whenever I use this, I get all the answers wrong. However, if I use

(vi)(sinx) - 1/2(gt) .. I get them right.

Is this a misprint?
 
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Probably not. It depends on how the angle is defined -- with respect to the horizontal, or with with respect to the vertical. These two definitions will affect whether the correct component is a sine or cosine of that particular angle.
 
You haven't given the context, but I can guess: This is the expression for the vertical component of velocity of an object hitting the ground for an object thrown with an initial velocity vi at an angle θ (measured with respect to horizontal).

If that's the case, your text is correct.
 
I think the textbook is right for the following reasons:
1. vf = vi + at and in your case, a = -g in y direction
2. s = (vi)*t + 1/2*g*(t^2), but the LHS of your equation is velocity and the power of t in your equation is 1.
 
Okay another equation in the book is

y = (vi)(sinx)(t) - 1/2(g)(t)^2 (unit here is meters)

If you divide out t on both sides you get meters over seconds and are left with (vi)(sinx) - 1/2gt

And meters/second is the unit for the original formula I posted. THe 1/2 is still there..
 
also: the angle is always with respect to the horizontal in these problems unless it's aviation (with bearings)
 
goochmawn314 said:
Okay another equation in the book is

y = (vi)(sinx)(t) - 1/2(g)(t)^2 (unit here is meters)

If you divide out t on both sides you get meters over seconds and are left with (vi)(sinx) - 1/2gt

And meters/second is the unit for the original formula I posted. THe 1/2 is still there..
The expression for altitude is correct. Your reasoning from that point on is incorrect. You need to take the derivative of the altitude to obtain the vertical component of velocity.

If you don't know what that means, you will eventually, but until then you'll have to take it for granted that the equations for altitude and the vertical component of velocity in your text are both correct.
 
Yeah the derivative is just gt isn't it.. Ok but in this course, there hasn't been any calculus yet. Thanks for your help
 

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