title: Math/Physics: Given angle and vector find point of intersection?
body: <p>I have two objects and I need to determine whether they will collide at some time in the future. Say the two objects are trucks, each in their separate lane. The first truck wants to change lanes, but will the trucks collide?</p>
  
  <p>Both objects are <strong>moving forward</strong>, but only the first has an angle. The objects are <strong>moving at different, varying velocities</strong>, yet only the velocity of the second object is known. Also, the two objects are operating on <strong>separate coordinate systems</strong> (meaning each object has a new origin), with varying distance between the objects.</p>
  
  <p>I don't have a vector for the first object, but I do have an angle (not fixed) at which it is headed, relative to the x-axis.</p>
  
  <p>For the second object, I have a vector, and it is headed straight.</p>
  
  <p>Please refer to the picture below:</p>
  
  <p><img src="https://i.stack.imgur.com/LM00H.png" alt="Collision"></p>
  
  <p>How can I find the point of intersection, based on these criteria? I imagine the angle is an infinite line, which at some point will cross the vector magnitude of the second object. I don't suppose this is as straight forward as calculating the point of intersection of two lines.</p>
  
  <p>Wrapup:</p>
  
  <ul>
  <li>Velocity of the second object is known (but varying)</li>
  <li>Angle of the first object is known</li>
  <li>Distance between the objects is known (but varying)</li>
  <li>Acceleration in the x-direction of the first object is known (But I <strong>CANNOT</strong> use this to find the velocity due to limitations)</li>
  </ul>