# Projectile Motion with Air Resistance problem

hi.
Suppose that a projectile of mass "m" is launched, from ground level in a horizontal plain, making an angle teta to the horizontal .(with air resistance).now in which angle "m" has the maximum range? .(our teacher said that we should find 53 degrees for teta).please prove it.
(first of all we should find (x-t) and (v-t) equations.then we should find the equation of range with those 2 equations and then we should derivative the rang equation(dr/d(teta).
so we will find the angle in which the mass "m" has the maximum range.this is my idia.if anyone knows the answer of this question,please tell it.i need the diagram of the motion too.)thanks alot. Last edited by a moderator:

I think this thread should be in the homework location... none the less you state with air resistance. My understanding is that the equation that describes air resistance is pretty complicated and is normally simplified to either linear or quadratic approximation. But newtons laws of motion with quadratic drag in horizontal and vertical motion results in a pair of differential equations that can only be solved numerically (there is no general solution).

tiny-tim
Homework Helper
Welcome to PF!

… our teacher said that we should find 53 degrees for theta …

Hi ahadpoolghaha! Welcome to PF! (I've always understood that it's 45 degrees without air resistance.)

What formula for air resistance did your teacher tell you to use? Hi ahadpoolghaha! Welcome to PF! (I've always understood that it's 45 degrees without air resistance.)

What formula for air resistance did your teacher tell you to use? I'm pretty sure that theta is always lower than 45 degrees with any plausible
formula for air resistance (linear, quadratic)