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proportional to vž, and that for the third block is proportional to v². If you fire at these 3 blocks one by one (separately) with the same initial speed of vo for your bullets, compute the farthest the bullet can travel in each of these all three cases.

proportional to vž, and that for the third block is proportional to v². If you fire at these 3 blocks one by one (separately) with the same initial speed of vo for your bullets, compute the farthest the bullet can travel in each of these all three cases.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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use the equation mdv/dt=-mg-kv to find the farthest distance, integrate with respect to x

 

use math differential calculus way and not a physics way

 

I want to see differential equations to arrive at the answer 

**Problem 4.4 (Textbook: Problem 2.4.16 on P121)**: Consider shooting a bullet of mass \( m \) to three different big blocks. The resistance (force) of the first block is assumed to be proportional to the bullet speed, that for the second block is proportional to \( v^{\frac{3}{2}} \), and that for the third block is proportional to \( v^2 \). If you fire at these 3 blocks one by one (separately) with the same initial speed of \( v_0 \) for your bullets, compute the farthest the bullet can travel in each of these three cases. Note that the gravitational force for this problem is negligible.
Transcribed Image Text:**Problem 4.4 (Textbook: Problem 2.4.16 on P121)**: Consider shooting a bullet of mass \( m \) to three different big blocks. The resistance (force) of the first block is assumed to be proportional to the bullet speed, that for the second block is proportional to \( v^{\frac{3}{2}} \), and that for the third block is proportional to \( v^2 \). If you fire at these 3 blocks one by one (separately) with the same initial speed of \( v_0 \) for your bullets, compute the farthest the bullet can travel in each of these three cases. Note that the gravitational force for this problem is negligible.
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