(b) Consider an object of mass m, dropped from some initial height and falling down towards Earth's surface with velocity v(t) at time t. Suppose we choose to model the force of air resistance as being proportional to the square of the instantaneous speed. (i) If we choose "up" to be the positive y direction and set ß> 0 to be a con- stant of proportionality, briefly explain why the most appropriate differential equation to model this setup is dv -mg+Bv² with v(0) = 0, dt rather than dv m- = -mg-Bv² with v(0) = 0. dt (ii) After setting m = 1, ß = 10 and g 10, solve this differential equation for the velocity of the object at time t. (iii) Determine the time at which the object reaches 90% of its terminal velocity. m-

(b) Consider an object of mass m, dropped from some initial height and falling down towards Earth's surface with velocity v(t) at time t. Suppose we choose to model the force of air resistance as being proportional to the square of the instantaneous speed. (i) If we choose "up" to be the positive y direction and set ß> 0 to be a con- stant of proportionality, briefly explain why the most appropriate differential equation to model this setup is dv -mg+Bv² with v(0) = 0, dt rather than dv m- = -mg-Bv² with v(0) = 0. dt (ii) After setting m = 1, ß = 10 and g 10, solve this differential equation for the velocity of the object at time t. (iii) Determine the time at which the object reaches 90% of its terminal velocity. m-

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.4: Total Differentials And Approximations

Problem 9E: Use the total differential to approximate each quantity. Then use a calculator to approximate the...

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