Discussion question from university physics

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SUMMARY

The discussion centers on calculating the time it takes for an object to fall from a height that is three times greater than a reference height, using the formula for displacement: displacement = V0t + 0.5g(t²). Participants derived initial times of T = √2 and T = √6 but struggled with setting up the proportion for the increased height. A suggestion was made to analyze the fall from various heights, specifically 1 m and 3 m, to clarify the relationship between height and time.

PREREQUISITES
  • Understanding of kinematic equations, specifically displacement equations.
  • Basic knowledge of gravitational acceleration (g = 9.8 m/s²).
  • Familiarity with the concept of free fall and time of descent.
  • Ability to manipulate algebraic expressions and proportions.
NEXT STEPS
  • Explore the derivation of the kinematic equation for free fall.
  • Learn how to set up and solve proportions in physics problems.
  • Investigate the effects of air resistance on falling objects.
  • Practice problems involving varying heights and their corresponding fall times.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and kinematics, as well as educators seeking to clarify concepts related to free fall and gravitational effects.

hagglebaby
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Homework Statement


When you drop an object from a certain height, it takes time T to reach the ground with no air resistance. If you dropped it from 3 times that height, how long (in terms of T) would it take to reach to the ground?


Homework Equations



displacement=V0t+.5g(t)2

The Attempt at a Solution



i got T=sqrt2 and T=sqrt6 but now I'm stuck on how to set up the next proportion. Also would like to see how you started this one.
 
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hagglebaby said:

Homework Statement


When you drop an object from a certain height, it takes time T to reach the ground with no air resistance. If you dropped it from 3 times that height, how long (in terms of T) would it take to reach to the ground?


Homework Equations



displacement=V0t+.5g(t)2

The Attempt at a Solution



i got T=sqrt2 and T=sqrt6 but now I'm stuck on how to set up the next proportion. Also would like to see how you started this one.

Perhaps you could consider the case of dropping a mass , on Earth where g = 9.8, from a height of 1 m and 3 m then 8 m and 24 m and see if that gives you any hints.
 
thank you! I think the answer is sqrt3
 

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