Thread: projectiles

A Rocket R is fired from ground with inital speed s to the horizontal at an angle . There is a resistive force F=-mkv where m is the mass and v is the vector (v1,v2) and K is a constant. Show the equations of motion are

and

My answer. First in the horizontal direction there is no resultant force so I don't get it

Originally Posted by Duke

A Rocket R is fired from ground with inital speed s to the horizontal at an angle . There is a resistive force F=-mkv where m is the mass and v is the vector (v1,v2) and K is a constant. Show the equations of motion are

and

My answer. First in the horizontal direction there is no resultant force so I don't get it

That is not true. The air resistance is given by



This force is proportional to the velocity in both of the x and y directions.

So in the y direction we have by newtons 2nd law



and in the x

How do you know the sign of kmv? Doesn't it needs to be negative.

Also I need to state inital conditions for v and r (vectors)

First I see why you are confused I factored out the minus signs in the force but forgot to put them in the final answer. Yes I had a typo and have edited the above post.

The initial conditions are implied not explicit given.

Assumption 1 Since we are free to setup our own coordinate system lets start the rocket at the origin. That would give the initial conditions.



Also since we are launching the rocket its initial velocity should also be zero

Thanks. If I define up as positive, do the signs change?

Originally Posted by Duke

Thanks. If I define up as positive, do the signs change?

No this set of equations defines up as positive in the y direction and right as positive in the x direction. You see this from the fact that -mg has a negative sign. If down were positive this would give the term mg.