Problems: Motion in Two dimensions including projectile motion

  1. A particle moving in the xy-plane has velocity components dx/dt = 6 + 2t and dy/dt = 4 + t
    where x and y are measured in metres and t in seconds.
    (i) Integrate the above equation to obtain x and y as functions of time, given
    that the particle was initially at the origin.
    (ii) Write the velocity v of the particle in terms of the unit vectors ˆi and ˆj .
  2. (iii) Show that the acceleration of the particle may be written as a = 2ˆi + ˆj .
  3. (v) Find the magnitude of the acceleration and its direction with respect to the x-axis.