2 projectiles, one at the origin the other at (0,100,0)m, have initial speeds of 35 m/s and 55 m/s respectively, and have direction cosine angles (45,60,60) and (60,135,60) respectively. Both are under the influence of gravity and experience a force of air resistance that has an acceleration of a = (-1, 0, -2.81) m/s^2. Assuming z>0, find:
a) The location both objects strike the ground
b) Where in space their paths cross, if they do.
S = Si + Vit + 1/2at^2 (Position equation)
Vf= Vi + at
D= Vit + 1/2at^2
The Attempt at a Solution
The work here is quite lengthy and it took me a while to write it down on paper. I am not asking for direct help in solving both a) and b) for this problem (but if possible it will be greatly appreciated). I just have an algebraic question for part b of this problem.
How do i go about in finding where two objects in 3d space cross? I took the substitution approach by making Path 1's total position = Path 2's total position in order to solve for one of the times. I used the quadratic formula, solved a time 2 then plugged it back to get time 1. Time 2 = 1.7098s and Time 1= 1.914s is what i got for the two times. What does this tell me though? they never meet? Or do i have to do something additional here? Also i have 3 equations here X direction, Y direction, and Z direction. When i did substitution method I only used Y direction to get T1 and I subbed it into the X direction equation to get the T2 number. Do I have to also use the Z direction equation, or is it ok to only use two equations?
Your feedback here would be much appreciated. Again I am not asking for help on solving this problem. Instead I am asking general algebra help in what approach to take in order to find when the two projectiles meet.