[2] Consider a projectile of mass m that is released from rest and allowed to fall under the influence of gravity and a linear in velocity air resistive force, f = -bu. (a) Draw a free-body diagram for the mass. (b) Setup N2 for the mass and convert it to a first order differential equation for velocity. Solve the differential equation. (c) Show that your result agrees with physical intuition for short times, i.e., for t small vygt. (d) Use your general result for velocity as a function of time to solve for the position as a function of time. (e) Again, show that your result for y(t) 1/2gt2 for short times.
[2] Consider a projectile of mass m that is released from rest and allowed to fall under the influence of gravity and a linear in velocity air resistive force, f = -bu. (a) Draw a free-body diagram for the mass. (b) Setup N2 for the mass and convert it to a first order differential equation for velocity. Solve the differential equation. (c) Show that your result agrees with physical intuition for short times, i.e., for t small vygt. (d) Use your general result for velocity as a function of time to solve for the position as a function of time. (e) Again, show that your result for y(t) 1/2gt2 for short times.
Related questions
Question
![[2] Consider a projectile of mass m that is released from rest and allowed to fall under the influence
of gravity and a linear in velocity air resistive force, f= -bu.
(a) Draw a free-body diagram for the mass.
(b) Setup N2 for the mass and convert it to a first order differential equation for velocity. Solve
the differential equation.
(c) Show that your result agrees with physical intuition for short times, i.e., for t small vy ≈ gt.
(d) Use your general result for velocity as a function of time to solve for the position as a function
of time.
(e) Again, show that your result for y(t)≈ 1/2gt²2 for short times.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c015292-e614-4754-9a92-673e636d111d%2F4a9b9a8b-8bc3-4de2-8c11-8be13cbe4317%2Fed2zmao_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[2] Consider a projectile of mass m that is released from rest and allowed to fall under the influence
of gravity and a linear in velocity air resistive force, f= -bu.
(a) Draw a free-body diagram for the mass.
(b) Setup N2 for the mass and convert it to a first order differential equation for velocity. Solve
the differential equation.
(c) Show that your result agrees with physical intuition for short times, i.e., for t small vy ≈ gt.
(d) Use your general result for velocity as a function of time to solve for the position as a function
of time.
(e) Again, show that your result for y(t)≈ 1/2gt²2 for short times.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 6 steps with 1 images
