https://r2.erweima.ai/mathbot/image/17248753822175gn7s99o.jpg

• i)¿Cu´ales de las siguientes ecuaciones son dimensionalmente correctas? (a) vf = vi + ax (b)
y = 2mcos(kx), donde k = 2m−1
. Donde m es metro, y x es una distancia.
• ii) La f´ormula siguiente es dimensionalmente correcta.
2
5
A
p
2gh − x
2 + P senα = QK, (1)
A es ´area; g es gravedad; h es la altura. ¿Cu´ales son las dimensiones de x, P y de Q si K/A tiene
dimensiones de masa?


The image presents a problem related to dimensional analysis in physics. Here’s a translation and breakdown of the problem:

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**Problem 2:**

1. **Which of the following equations are dimensionally correct?**
   - (a) \( v_f = v_i + ax \)
   - (b) \( y = 2m \cdot \cos(kx) \), where \( k = 2m^{-1} \). Here, \( m \) represents meters, and \( x \) is a distance.

2. **Is the following formula dimensionally correct?**

   \[
   \frac{2}{5} A \sqrt{2gh - x^2} + P \sin \alpha = QK
   \]
   
   Where:
   - \( A \) is the area,
   - \( g \) is the acceleration due to gravity,
   - \( h \) is the height.

   What are the dimensions of \( x \), \( P \), and \( Q \) if \( K/A \) has dimensions of mass?

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### Steps to Solve:

1. **For Part 1:**
   - Check the dimensions of each term in the given equations and ensure they match.

2. **For Part 2:**
   - Analyze the formula by equating the dimensions on both sides and deduce the dimensions of \( x \), \( P \), and \( Q \) accordingly.

Would you like to proceed with detailed solutions for each part?

Explore dimensional analysis in physics with detailed solutions to dimensional correctness of equations. This problem covers physics equations involving dimensional analysis and provides insights into solving such problems effectively.

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