Question

Two airplanes leave an airport at the same time. The velocity of the first airplane is 650 m/h at a heading of 60.5 ◦ . The velocity of the second is 560 m/h at a heading of 85◦ . How far apart are they after 2.9 h? Answer in units of m.

Answer 1

First, illustrate the problem as shown in the attached picture. Next, let's find the distance traveled by planes A and B after 2.9 h.

Distance of A: 650 m/h * 2.9 h = 1,885 m
Distance of B: 560 m/h * 2.9 h = 1,624 m

Then, we use the cosine law to determine the distance x. The angle should be: 85 - 60.5 = 24.5°

x² = 1,885² + 1,624² - 2(1,885)(1,624)(cos 24.5°)
x = √619381.3183
x = 787 m