How long before the box hits the ground?

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Discussion Overview

The discussion revolves around calculating the time it takes for a box dropped from a plane traveling at 100 m/s from an elevation of 2000 meters to reach the ground. The focus includes the application of physics equations related to freefall and the effects of air resistance.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant presents the problem of a box dropped from a plane and asks for the time to reach the ground.
  • Another participant suggests applying the freefall equation and multiplying the time by the speed of the plane, implying a connection between vertical and horizontal motion.
  • A different participant questions the assumptions made, particularly regarding air resistance, and states that if air resistance is ignored, the acceleration due to gravity can be considered constant at 9.8 m/s².
  • This participant provides a calculation framework, stating that the time to hit the ground can be derived from the equation 4.9 t² = 2000, focusing solely on vertical motion.
  • A later reply acknowledges a misunderstanding of the problem, indicating that the horizontal speed of the box is irrelevant to the time it takes to fall, as the time depends only on vertical acceleration and speed.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of horizontal speed and the assumptions regarding air resistance. The discussion remains unresolved regarding the implications of these factors on the time calculation.

Contextual Notes

Assumptions about air resistance and its potential impact on the calculations are not fully explored, and the relevance of horizontal motion to the time of descent is contested.

unidentified4789
A plane is traveling at 100m/s when it drops a box at an elevation of 2000 meters. How much time is required for the box to reach the earth?
 
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You know the equation for freefall? Apply it to find the time and multiply the time by the speed of the plane.
 
What assumptions are you making? Are you ignoring air resistance? (If not, then you will have to state what the air resistance is.)

Assuming no air resistance, 2000 m is low enough that we can ignore the change in gravitational force due to change in distance so: the acceleration is 9.8 m/s2. The downward speed after time t is 9.8 t m/s and the distance fallen is 4.9 t2. The box will hit the Earth when 4.9 t2= 2000.

The information about the horizontal speed of the airplane (and therefore the horizontal speed of the box) is irrelevant. The time to hit depends only on vertical acceleration and speed.
 
As someone informed me in a pm, I misread the problem. Sorry. Halls had it right. I was thinking of how far the box would move forward.
 

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