find path of a particle projected with vel`v, at angle x to the hori?

Question

Find the path of a particle projected with a velocity v at angle x to the horizon in a medium, whose resistance, apart from gravity, varies as velocity. Also find the greatest height attained

Answer 1

If there was no air resistance, it's a parabola, and it's not hard to work out the equation of the trajectory. However, with air resistance factored in, the derivation of the equation of the trajectory is horrendous, and it's not a parabola, and there is no easy way to do it. There's too little space here for the complete derivation, so consult the wiki article about it, at the bottom where it says, "Trajectory of a projectile with air resistance". Also, air resistance should vary with the SQUARE of the velocity, it's not a linear function.

Answer 2

try this way..ur particle taces a parabolic path .since the particle is projected at an angle , break ur vellocity into 2 components.
1. horizontal comp VCOSx,2.vertical compt VSINx.
THE VERTICAL COMP MOVES WITH UNIFORM VELLOCITY
THE HORIZONTAL COMPT GETS EFFECTED BY THE acc and medium resistance.
now use the parabolic formula to relate dis,vel,acc& res of medium.
by using the vertical comp get the maxium ht attained!