- #1
pingpong240
- 27
- 0
Here's the question:
An antiaircraft gun fires shells at 200 m/s at a 60° angle. An enemy plane flies directly toward the gun at 300 m/s, 495 m off the ground. How far away (horizontally) must the plane be when the gun fires for the shell to hit the plane?
First off, I know I get two solutions here. I believe it's because of the trajectory of the shell as it hits the plane on the way up or on the way down.
Knowns
v_ix = 200cos(60) = 100
v_iy = 200sin(60)
a_x = 0
a_y = -9.81
y=485 m
Unknowns
x
v_fy
v_fx
t
Equations
y_f = y_i + v_iy * t + .5at^2
x_f = x_i + v_ix * t + .5at2
I'm not sure if I really have to take into account the -300 m/s of the plane, but here's what I've tried so far:
I used the above equation for the y direction to get
485 = 200sin(60)t -4.9t^2
0 = -4.9t^2 + 200sin(60)t-485
I used the quadratic equation to get two times, 3.066 s and 32.2819 s. I tried fitting these into the x direction equation above, but no luck. I may have done something wrong up to this point, but I think that where I go next is where my problems are occurring. I ended up getting 306.61 for the first distance and 3228 for the second, obviously nothing there. Please help me with the rest of the problem!
An antiaircraft gun fires shells at 200 m/s at a 60° angle. An enemy plane flies directly toward the gun at 300 m/s, 495 m off the ground. How far away (horizontally) must the plane be when the gun fires for the shell to hit the plane?
First off, I know I get two solutions here. I believe it's because of the trajectory of the shell as it hits the plane on the way up or on the way down.
Knowns
v_ix = 200cos(60) = 100
v_iy = 200sin(60)
a_x = 0
a_y = -9.81
y=485 m
Unknowns
x
v_fy
v_fx
t
Equations
y_f = y_i + v_iy * t + .5at^2
x_f = x_i + v_ix * t + .5at2
I'm not sure if I really have to take into account the -300 m/s of the plane, but here's what I've tried so far:
I used the above equation for the y direction to get
485 = 200sin(60)t -4.9t^2
0 = -4.9t^2 + 200sin(60)t-485
I used the quadratic equation to get two times, 3.066 s and 32.2819 s. I tried fitting these into the x direction equation above, but no luck. I may have done something wrong up to this point, but I think that where I go next is where my problems are occurring. I ended up getting 306.61 for the first distance and 3228 for the second, obviously nothing there. Please help me with the rest of the problem!