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5. For high-speed motion through the air-such as a skydiver falling before the parachute is opened-air resistance is closer to a power of the instantaneous velocity v(t). Determine a differential equation for the volocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity.

5. For high-speed motion through the air-such as a skydiver falling before the parachute is opened-air resistance is closer to a power of the instantaneous velocity v(t). Determine a differential equation for the volocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity.

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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Answer Quetion 5 pls

1. The population model given in class fails to take death into consideration; the growth rate equals the birth rate. In another model of a changing population of a community it is assumed that the rate at which the poplation changes is a net rate-that is, the difference between the rate of births and the rate of deaths in the community. Determine a model for the population P(t) if both the birth rate and the death rate are proportional to the population present at time t. 2. Using the concept of net rate above, determine a model for a population P(t) if the birth rate is proportional to the population present at time t but the death rate is proportional to the square of the population present at time t. 3. At a time denoted as t = 0 a technological innovation is introduced into a community that has a fixed population of n people. Determine a differential equation for the number of people x(t) who have adopted the innovation at time t if it is assumed that the rate at which the innovations spread through the community is jointly proportional to the number of people who have adopted it and the number of people who have not adopted it. dP = (k cos t) P, where k is a positive constant, is a model of human population P(t) 4. The differential equation of a certain community. Discuss an interpretation for the solution of this equation. In other words, what kind of population do you think the differential equation describes? dt 5. For high-speed motion through the air-such as a skydiver falling before the parachute is opened-air resistance is closer to a power of the instantaneous velocity v(t). Determine a differential equation for the volocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity.
Transcribed Image Text:1. The population model given in class fails to take death into consideration; the growth rate equals the birth rate. In another model of a changing population of a community it is assumed that the rate at which the poplation changes is a net rate-that is, the difference between the rate of births and the rate of deaths in the community. Determine a model for the population P(t) if both the birth rate and the death rate are proportional to the population present at time t. 2. Using the concept of net rate above, determine a model for a population P(t) if the birth rate is proportional to the population present at time t but the death rate is proportional to the square of the population present at time t. 3. At a time denoted as t = 0 a technological innovation is introduced into a community that has a fixed population of n people. Determine a differential equation for the number of people x(t) who have adopted the innovation at time t if it is assumed that the rate at which the innovations spread through the community is jointly proportional to the number of people who have adopted it and the number of people who have not adopted it. dP = (k cos t) P, where k is a positive constant, is a model of human population P(t) 4. The differential equation of a certain community. Discuss an interpretation for the solution of this equation. In other words, what kind of population do you think the differential equation describes? dt 5. For high-speed motion through the air-such as a skydiver falling before the parachute is opened-air resistance is closer to a power of the instantaneous velocity v(t). Determine a differential equation for the volocity v(t) of a falling body of mass m if air resistance is proportional to the square of the instantaneous velocity.
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