m An object with mass 64kg has an initial downward velocity of 69. Assume that the atmosphere exerts S a resistive force with magnitude proportional to the speed. The resistance is - 50N when the velocity is m m -5. Use g = 10- S 8² a. Write out a differential equation in terms of the velocity v, and acceleration a. b. Find the velocity v(t) for the object.
m An object with mass 64kg has an initial downward velocity of 69. Assume that the atmosphere exerts S a resistive force with magnitude proportional to the speed. The resistance is - 50N when the velocity is m m -5. Use g = 10- S 8² a. Write out a differential equation in terms of the velocity v, and acceleration a. b. Find the velocity v(t) for the object.
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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![### Problem Statement:
An object with mass \( 64 \, \text{kg} \) has an initial downward velocity of \( -69 \, \frac{\text{m}}{\text{s}} \). Assume that the atmosphere exerts a resistive force with magnitude proportional to the speed. The resistance is \( -50 \, \text{N} \) when the velocity is \( -5 \, \frac{\text{m}}{\text{s}} \). Use \( g = 10 \, \frac{\text{m}}{\text{s}^2} \).
### Tasks:
**a. Write out a differential equation in terms of the velocity \( v \), and acceleration \( a \).**
[Write your answer here]
**b. Find the velocity \( v(t) \) for the object.**
[Write your answer here]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d3733a5-5e9e-433b-b6d1-2cfec636672d%2F98e3a78a-35e1-4c16-b0d7-d6078f8ef24e%2Fzxu55j9_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
An object with mass \( 64 \, \text{kg} \) has an initial downward velocity of \( -69 \, \frac{\text{m}}{\text{s}} \). Assume that the atmosphere exerts a resistive force with magnitude proportional to the speed. The resistance is \( -50 \, \text{N} \) when the velocity is \( -5 \, \frac{\text{m}}{\text{s}} \). Use \( g = 10 \, \frac{\text{m}}{\text{s}^2} \).
### Tasks:
**a. Write out a differential equation in terms of the velocity \( v \), and acceleration \( a \).**
[Write your answer here]
**b. Find the velocity \( v(t) \) for the object.**
[Write your answer here]
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