Question

Problem 4: This is a very straightforward relative velocity problem, but let's make sure it gets done correctly. First, notice that there is no given, or inherent, coordinate system. You need to define a coordinate system--I'd suggest a regular x-y Cartesian system. Once you've done that you need to project the given velocities of the planes into the system you just defined. For example, if your x-axis is positive to the right, then the velocity vector of plane A is v_A = 800i + 0j. Do this for both planes in your coordinate system and then use the relative velocity equation v_B = v_A + v_B/A to determine the velocity of B relative to A. This is the velocity that B is moving away from A. As such this velocity vector, multiplied by time, gives the displacement (change of position) between the two planes. The components of displacement will depend on your coordinate system choice, but you should find the magnitude of the displacement is just over 21 km. Careful on this one: Make sure not to drop negatives, since you may have double negatives which should become positive in this problem!

4. In Figure 3 plane A flies at a constant 800 km/h due east while plane B flies at a constant 575 km/h southwest. The planes are flying at the same constant altitude. Determine the change in position of plane B relative to plane A which takes place during a 1-minute interval. Note: Your answer should be in vector form. Make sure to define your coordinate system! Figure age 1 of2

Answer 1

Given V_A = 500km/h = 50/6km/min V_B = 575km/h = 115/12km/min V_A = 50/6i V_B = -V_Bcos 45i-V_Bsin 45j V_B = -6.7764i-6.7764j V_B/A = V_B-V_A = (-6.7764i-6.7764j)-(50/6i) V_B/A = -15.11i-6.7764j km/min dr_B/A/dt = -15.11i-6.7764j r_B/A = -15.11ti-6.7764tj At t = 1min r_B/A = -15.11i-6.7764j