Caída libre | Ejemplo 1 Se deja caer... @MatematicasprofeAlex

Main ideas / lessons

• Purpose of the video: Show how to solve free-fall problems step-by-step, assuming the viewer has already learned the basics (gravity, free fall, sign conventions, and formulas) in previous videos.
• Key interpretation of “dropped / it falls”:
  • Usually implies the object starts from rest → initial velocity (v_0 = 0) (unless the problem states it’s in a vehicle/balloon/aircraft, which could change the initial velocity).
  • The movement begins immediately when it is dropped.
• Given vs. missing information:
  • For the first exercise (building height), the problem gives:
    • Initial velocity (via “dropped” and standing still) → (v_0 = 0)
    • Time to reach the ground → (t = 4\,s)
    • Gravity assumed on Earth → (g \approx 9.8\,m/s^2)
  • The question asks for height, while final velocity is not given/needed.
  • The missing “third” needed piece is essentially height—which is what you solve for (while ensuring you don’t accidentally choose a formula that requires final velocity).
• Sign convention / direction:
  • When motion is downwards and speed increases:
    • Take downward as positive.
    • Acceleration (gravity) is positive in that direction.
  • Gravity becomes negative if the motion is upwards (mentioned for later videos).
• Units discipline (strong emphasis):
  • Before substituting, ensure all quantities are in meters and seconds.
  • If not, convert (e.g., kilometers → meters, hours/days → seconds).
  • The speaker prefers substituting only the numerical magnitudes, not the units inside calculations, as long as units are correct.

Methodology / step-by-step instructions (detailed)

Exercise 1: Find the height of the building

1. Read the statement and list known data

   • “Stone is dropped from the top of a building” ⇒ object is initially stationary:
     • (v_0 = 0\,m/s)
   • “Reaches the ground after 4 seconds”:
     • (t = 4\,s)
   • “On Earth” ⇒ use:
     • (g = 9.8\,m/s^2)
   • Unknown:
     • Height (y) (or (h)

2. Choose the correct kinematics formula

   • Identify what you do not have and do not want:
     • Final velocity is not needed/available.
   • Therefore, select the formula that does not include final velocity and can solve for height.

3. Copy the chosen formula into your notebook (recommended)

4. Check unit consistency (meters and seconds)

5. Substitute values (using magnitudes)

   • Apply:
     • Terms like (0 \cdot t) become (0)
   • Compute time-squared directly:
     • (t^2 = 4^2 = 16)

6. Do arithmetic carefully

   • Split operations to avoid errors.
   • Use simplifications where possible (e.g., divide factors before multiplying).

7. Final answer

   • Report in words and with units:
     • Height of the building (= 78.4\,m)

Exercise 2 (practice within the same video): Find impact speed

1. Read the statement and list known data

   • “A child drops a toy from his bedroom window”:
     • “Drops” ⇒ (v_0 = 0\,m/s)
     • Motion is downwards, gravity increases speed:
       • take downward as positive
   • “Took 3 seconds to reach the ground”:
     • (t = 3\,s)
   • Earth gravity:
     • (g = 9.8\,m/s^2)
   • Unknown:
     • Final velocity (v) (the speed at impact)

2. Choose the formula that avoids height

   • Since height is not provided and the question asks for final velocity:
     • Select the kinematics equation that does not include height.

3. Copy the chosen formula (recommended)

4. Check units (meters and seconds)

5. Substitute and compute

   • With (v_0 = 0):
     • (v = v_0 + g t = 0 + 9.8 \cdot 3)
     • (v = 29.4\,m/s)

6. Final answer

   • Give it in words and units:
     • The toy hits the ground with velocity 29.4 m/s.

Speakers / sources

• Speaker: “MatematicasprofeAlex” (the channel/instructor implied by the title: @MatematicasprofeAlex)