Solving Free-fall: 10kg Object Dropped from Great Height

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SUMMARY

The discussion centers on solving a physics problem involving a 10 kg object dropped from a great height, subjected to air resistance proportional to its velocity. The equation used is 10(dv/dt) = 98 - 10v, which represents the forces acting on the object. Participants express confusion over integrating factors and separable equations, indicating a need for clarity on the solution process and the correct application of differential equations in this context.

PREREQUISITES
  • Understanding of Newton's second law of motion
  • Familiarity with differential equations
  • Knowledge of integrating factors and separable equations
  • Basic principles of kinematics and dynamics
NEXT STEPS
  • Study the application of Newton's second law in variable resistance scenarios
  • Learn about solving first-order linear differential equations
  • Explore the concept of terminal velocity and its implications in free-fall problems
  • Practice problems involving air resistance and motion equations
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Students studying physics, educators teaching dynamics, and anyone interested in solving real-world problems involving motion and resistance.

darthxepher
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I am having trouble on this problem.

An object of mass 10 kg is dropped from a great height. (a) If the object is subjected to air resistance equivalent to 10 times the instantaneous velocity, find the velocity. (b) How far does the object drop after 5 sec?

Ok so I thought the equation would be:

10(dv/dt) = 98-10v

but when i do the integrating factor or seperable i don't get the answer. Can someone tell me what i am doing wrong.
 
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We keep getting questions like this. NO, no one can tell you what you are doing wrong because we don't know what you are doing! Please show (i) how you solved this problem, (ii) what you got as a solution, (iii) why you think that is wrong.
 
(i) how you solved this problem,

An object of mass 10 kg is dropped from a great height. (a) If the object is subjected to air resistance equivalent to 10 times the instantaneous velocity, find the velocity. (b) How far does the object drop after 5 sec?

(ii) what you got as a solution,

Don't know how to start.

(iii) why you think that is wrong.
 

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