A Certain Freely Falling Object Requires 110 S To Travel

A Certain Freely Falling Object Requires 110 S To Travel The Last

A free-falling object requires 1.10 seconds to travel the last 40.0 meters before hitting the ground. The task is to determine the initial height above the ground from which the object was dropped.

Assuming constant acceleration due to gravity (g = 9.80 m/s²), we analyze the motion starting from the point where the object is at height h, with initial velocity v₀ = 0 (since it is dropped). The distance traveled during time t is given by:

s = v₀ t + (1/2) g t²; since v₀=0, s = (1/2) g t².

However, because we're given the time to travel the last 40.0 meters, we consider the motion during the final segment, starting at a height h₁ where the object is 40.0 meters above the ground, moving downward with velocity v at that moment, and traversing the last 40.0 meters in 1.10 seconds.

First, compute the velocity at the start of the last 40.0 meters:

v = g t_last = 9.80 m/s² × 1.10 s ≈ 10.78 m/s.

Next, determine the height h₁ where the object begins its last 40 meters:

h₁ = v t_last + (1/2) g t_last² ≈ 10.78 × 1.10 + 0.5 × 9.80 × (1.10)² ≈ 11.86 + 5.92 ≈ 17.78 meters.

Since h₁ is at 17.78 meters above the ground, and the last 40 meters are traveled in 1.10 seconds, we can now find the total height h from which the object was dropped.

The velocity at height h₁ is v, and the total height h can be found from energy or kinematic equations:

v² = 2 g (h - h₁). We already have v ≈ 10.78 m/s, so

h - h₁ = v² / (2 g) = (10.78)² / (2 × 9.80) ≈ 116.22 / 19.6 ≈ 5.93 meters.

Therefore, the initial height h is:

h = h₁ + 5.93 ≈ 17.78 + 5.93 ≈ 23.71 meters.

Answer: The object was released from approximately 23.71 meters above the ground.

Sample Paper For Above instruction

Analysis of Free Fall from Specific Heights and Related Kinematic Problems

The physics of free fall involves understanding how objects accelerate under gravity when no other forces, such as air resistance, significantly influence their motion. Applying kinematic equations allows us to analyze various problems involving free-falling objects, such as determining initial heights, velocities, and the effects of motion segments.

In the case examined, a freely falling object takes 1.10 seconds to travel the last 40 meters before impact. By leveraging this timing and the known acceleration due to gravity, it is possible to trace back to the initial release point. The process involves calculating the velocity at the beginning of the last segment, then deducing the height where this velocity was attained, and subsequently the total initial height from which the object was released.

The calculation begins with understanding the velocity during the last 40 meters: since the object takes 1.10 seconds to cover this distance while accelerating under gravity, its velocity at the start of this segment is approximately 10.78 m/s. Using the kinematic relationship v² = 2 g (h - h₁), the height difference from the starting point of the last segment to the initial height is approximate 5.93 meters. Adding this to the height at the beginning of the final segment yields an initial height of roughly 23.71 meters.

This problem exemplifies the application of kinematic equations to real-world physics problems involving free fall, enabling various critical analyses such as estimating the height from which an object is dropped, understanding velocity profiles, and analyzing the motion in stages.

Understanding these principles is essential in diverse fields, including engineering, safety analysis, and even sports science, where the motion of falling objects under gravity plays a significant role.

References

  • Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers with Modern Physics. Cengage Learning.
  • Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of Physics. Wiley.
  • Tipler, P. A., & Mosca, G. (2008). Physics for Scientists and Engineers. W. H. Freeman.
  • Giancoli, D. C. (2013). Physics: Principles with Applications. Pearson.
  • Young, H. D., & Freedman, R. A. (2012). University Physics with Modern Physics. Pearson.
  • Walker, J. (2005). Physics. Pearson Education.
  • Knight, R. D. (2017). Physics for Scientists and Engineers: A Strategic Approach. Pearson.
  • Heathcote, R. G. (2010). Classical Mechanics for Physics Students. Cambridge University Press.
  • Tipler, P. A., & Llewellyn, R. (2012). Modern Physics. W. H. Freeman.
  • Hewitt, P. G. (2014). Conceptual Physics. Pearson.

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