Solving First-Year Physics Textbook Puzzle: Adding Squared Equations

In summary, the conversation involves trying to solve a physics problem from a textbook, but the person was unable to find a solution even after spending an hour. They discuss equations involving v1f and v2f, and eventually try squaring and adding the equations. They realize that the simplified equation is derived from the original equations and involves a mistake they made in their calculations. The conversation ends with a realization of their mistake and a grateful thanks for pointing it out.
  • #1
mohdhm
42
0
ok this is in an example in a first-year physics textbook, yet some how i spent an hour trying to solve it (identities, tricks, etc) and could not find a solution.

here is what the textbook states:
(1) v2f*cos[tex]\phi[/tex] = 3.5*10^5 - v1f*cos(37)
(2) v2f*cos[tex]\phi[/tex] = v1f*sin(37)

"now we sqaure these two equations and add them"

= 1.23*10^11 - 7*10^5*v1f*cos(37) + v1f^2*cos(37)^2 + v1f^2*sin(37)^2

(then it simplifies further)

I know that 1.23*10^11 is (3.5*10^5)^2 and that 7*10^5 is 2*3.5*10^5any help in explaining how this equation is derived would be a great help (ESPECIALLY how 7*10^5 seems to pop out of no where)
 
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  • #2
Did you try squaring and adding the terms?
 
  • #3
mohdhm said:
any help in explaining how this equation is derived would be a great help (ESPECIALLY how 7*10^5 seems to pop out of no where)

More importantly, where did that cos(37) come from?
 
  • #4
sorry the cos 35 is supposed to be cos 37. my mistake.

Yes i did try adding them and squaring them. your point? why the **** would i take the time to ****ing type it down clearly for your convenience.
 
  • #5
mohdhm said:
Yes i did try adding them and squaring them. your point?
You obviously missed something doing that. Remeber that -2ab when expanding (a-b)^2?
 
  • #6
lol, you know what... i didn't forget that i should get -2ab... i made an even dumber mistake... i did (a^2 - b^2)

wow... thanks for pointing it out though, holy crap.
 

FAQ: Solving First-Year Physics Textbook Puzzle: Adding Squared Equations

What is the purpose of solving first-year physics textbook puzzles?

The purpose of solving first-year physics textbook puzzles is to develop critical thinking skills and deepen understanding of fundamental physics concepts. These puzzles often involve applying mathematical equations and principles to solve real-world problems.

How do you approach solving first-year physics textbook puzzles?

The best approach for solving first-year physics textbook puzzles is to first carefully read and understand the given problem. Then, identify the relevant equations and principles that can be used to solve the problem. It is also helpful to draw diagrams or make a list of known and unknown quantities. Finally, apply the equations and solve for the unknown quantity.

What are some common challenges when solving first-year physics textbook puzzles?

Some common challenges when solving first-year physics textbook puzzles include understanding the problem statement, selecting the appropriate equations, and correctly applying those equations. It is also important to pay attention to units and ensure they are consistent throughout the problem. Additionally, some puzzles may involve multiple steps, so it is important to check the final answer and ensure it makes sense.

How does solving first-year physics textbook puzzles relate to real-world applications?

Solving first-year physics textbook puzzles helps develop problem-solving skills that are essential in many real-world applications. These puzzles often involve applying physics principles to solve practical problems, such as calculating the trajectory of a projectile or determining the forces acting on an object. The critical thinking skills developed through solving these puzzles can also be applied to various fields, including engineering, medicine, and research.

Are there any tips or strategies for solving first-year physics textbook puzzles?

One helpful tip for solving first-year physics textbook puzzles is to break the problem down into smaller, more manageable parts. This can make the problem seem less daunting and allow for a clearer understanding of the steps involved. It is also important to double-check calculations and units throughout the problem-solving process. Additionally, practicing regularly and seeking help from peers or instructors can also improve problem-solving skills.

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