Question

Two dimensional motion with air drag (think golf ball trajectory) is not integrable, but purely horizontal motion and purely vertical motion are separately integrable. 1. A railroad boxcar of mass $m$ on a level frictionless track has initial speed $v_0$ at the origin. There is an aerodynamic drag force $-cv\vec{v}$ acting horizontally. Find (a) $v(t)$ (b) $x(t)$ (c) What is the furthest distance the boxcar travels? (d) $v(x)$

          Two dimensional motion with air drag (think golf ball trajectory) is not integrable, but purely horizontal motion and purely vertical motion are separately integrable.
1. A railroad boxcar of mass $m$ on a level frictionless track has initial speed $v_0$ at the origin. There is an aerodynamic drag force $-cv\vec{v}$ acting horizontally. Find
(a) $v(t)$
(b) $x(t)$
(c) What is the furthest distance the boxcar travels?
(d) $v(x)$

Two dimensional motion with air drag (think golf ball trajectory) is not integrable, but purely horizontal motion and purely vertical motion are separately integrable.
1. A railroad boxcar of mass m on a level frictionless track has initial speed v0 at the origin. There is an aerodynamic drag force -cvv⃗ acting horizontally. Find
(a) v(t)
(b) x(t)
(c) What is the furthest distance the boxcar travels?
(d) v(x)

Added by Kevin S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Timothy James

02/07/2023

Step 1

The equation of motion for the boxcar in the horizontal direction can be written as: m(dv/dt) = -cv where v is the velocity of the boxcar, c is the drag coefficient, and m is the mass of the boxcar. Show more…

Show all steps

Thanks for your feedback!

Two dimensional motion with air drag (think golf ball trajectory) is not integrable, but purely horizontal motion and purely vertical motion are separately integrable. A railroad boxcar of mass m on a level frictionless track has initial speed v_(0) at the origin. There is an aerodynamic drag force -cvvec(v) acting horizontally. Find (a) v(t) (b) x(t) (c) What is the furthest distance the boxcar travels? (d) v(x) Two dimensional motion with air drag (think golf ball trajectory) is not integrable, but purely horizontal motion and purely vertical motion are separately integrable. 1. A railroad boxcar of mass m on a level frictionless track has initial speed vo at the origin. There is an aerodynamic drag force -cuy acting horizontally. Find (a)v(t) (b) x(t) (c) What is the furthest distance the boxcar travels? (d) v(x)