Motion in Two and Three Dimensions and airplane

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Discussion Overview

The discussion revolves around calculating the distance at which an airplane should release a bomb to hit a target while in level flight at a specified altitude and speed. The focus includes mathematical reasoning and problem-solving techniques related to motion in two dimensions.

Discussion Character

  • Mathematical reasoning
  • Homework-related
  • Technical explanation

Main Points Raised

  • One participant attempts to use the equation x - x0 = (v0)(cos(theta))t but finds it does not yield the correct answer.
  • Another participant proposes a method assuming the bomb is in free fall, calculating the time of fall using h = 0.5 * g * t^2, and then determining the horizontal distance traveled during that time.
  • A different participant claims to have arrived at an answer of 417 m through their method, which involves converting the airplane's speed to meters per second and applying it to the time of fall.
  • Another participant calculates the distance as 414.1 m, noting a unit conversion error in their earlier calculations.
  • One participant confirms the 417 m answer, correcting their own unit conversion mistake and expressing frustration with the problem.

Areas of Agreement / Disagreement

There is no consensus on the exact distance, with participants arriving at slightly different values (414.1 m and 417 m) and acknowledging errors in unit conversions. Multiple competing views on the calculation methods remain present.

Contextual Notes

Participants express uncertainty regarding unit conversions and the application of equations, indicating that assumptions about the motion and gravitational effects may not be fully resolved.

Who May Find This Useful

This discussion may be useful for students or individuals interested in physics problems related to projectile motion and the application of kinematic equations in real-world scenarios.

patelkey
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The airplane shown is in level flight at an altitude of 0.50 km and a speed
of 150 km/h. At what distance d should it release a heavy bomb to hit the
target X?

-I tried using x-x0=(v0)(cos(theta))t; and then solving for t with another equation but that does not give me the correct answer when I solve for x. Any suggestions?
 
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Assume it isn't moving for a second. h=500m=0.5*g*t^2 => t=sqrt(2*500m/(10m/s^2)). So it will be in the air for this long. Now assume it is moving along the x-axis for this period of time, t. The distance it will travel will simply be t*(horizontal speed). So if it is moving at 2.5km/s, the distance d will be (2.5km/s)*sqrt(2*500m/(10m/s^2)).

Does this help?
 
No I actually got that answer through a different method, however, the correct answer is 417 m.
 
I'm getting the correct answer to be 414.1m, and that is using what I explained earlier. Except I converted units wrong because I'm tired. :) 150km/h = 41m/s

d=(41m/s)*sqrt(2*500m/(9.8m/s^2))=414m. This is definitely correct.
 
150km/h=41.6666667m/s
==>
d=(41.6666667m/s)*sqrt(2*500m/(9.8m/s^2))=417m

Thar's your 417m.
 
Wow your right
I also converted units wrong
this problem was really annoying,
thanks for the help!
 

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