Complete Square + Leibniz question (2 questions)

  • #1

Homework Statement


1. How did they complete the square for these equations in the picture below? What was their thought process?

2. distance/velocity = time , velocity/acceleration = time , In leibniz notation how does this cancel out?

When you divide, how does it cancel out to give you a time unit?

Homework Equations


1. In picture

2. ds/dt / d2s / dt2

The Attempt at a Solution


1. It seems like it came out of thin air.

2. dt/ds = time?
 

Attachments

Answers and Replies

  • #2
BiGyElLoWhAt
Gold Member
1,570
116
What is 2. in your relevant equations?

##V = d/t \to t = d/V##
You can add A and subtract A (equivalent to adding 0), and it's still the same.
##\frac{v_{y0}x}{v_{x0}} - \frac{gx^2}{2v_{x0}^2} + \frac{v_{y0}^2}{2g} - \frac{v_{y0}^2}{2g} ##
They factored out ## \frac{-g}{2v_{x0}^2} ##

Rearrange it and it might look a little closer.
 
  • #3
In my relevant solutions it is velocity/acceleration, the way I put it was just in leibniz notation in terms of s(t)
 
  • #4
BiGyElLoWhAt
Gold Member
1,570
116
I think I was just confused by all the slashes. Sort of makes it look like one big fraction made of fractions.
 
  • #5
V2y0/2g

How did you find that
 
  • #6
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,581
6,450
V2y0/2g

How did you find that
I assume you are asking about getting from the second equation in the image to the third.
Just expand the square in the third equation and simplify. You should arrive at the second equation.
 

Related Threads on Complete Square + Leibniz question (2 questions)

  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
873
Replies
6
Views
2K
  • Last Post
Replies
0
Views
950
  • Last Post
Replies
3
Views
2K
Replies
1
Views
2K
  • Last Post
Replies
3
Views
2K
Replies
4
Views
2K
Top