A particle moves in a vertical plane under gravity and an air resistance whose magnitude per unit mass is k times the speed of the particle, where k is a positive constant. The coordinates of the particle at time t, with respect to a horizontal axis Ox and a vertically upward axis Oy, are (x,y).

Show that

d^2 x /dt^2 = -k dx/dt

d^2y/dt^2 = - k dy/dt - g ...... (*)

Given that a projectile with a terminal speed of 30.5 m/s is fired when t=0 from O with an initial speed of 30.5 m/s at an inclination of 45 degree.

(a)Solve (*) for x and y in term of t.
(b) Plot the trajectory of the projectile.
(c) Compare the path trajectory to that when there is no air resistance.

Similar Questions
    1. answers icon 1 answer
  1. Question 15An airplane moves 268 m/s as it travels around a vertical circular loop which has a radius of 1.9 km. The
    1. answers icon 2 answers
  2. An airplane moves 243 m/s as it travelsaround a vertical circular loop which has a radius of 1.2 km. What is the magnitude of
    1. answers icon 2 answers
  3. The magnitude of the velocity of a particlewhich starts from rest 2 ft below the origin when t = 0 and moves along a vertical
    1. answers icon 4 answers
more similar questions