Question

Plane A flies at a velocity of  m/s relative to Plane B. Plane B flies at a velocity of  m/s relative to Plane C. What is the velocity of Plane A relative to Plane C? Estimate the speed of light in a vacuum as 3.00 × 108m/s.

Answer 1

First, assume the planes fly along the same straight line. Thus, if velocity of plane C is $\nu$ m/s, and the plane B flies b m/s relative to C, the speed of B is

$$\vec{v}_B=\vec{\nu}+\vec{b}.$$

And since plane A flies at speed a relative to B, the speed of A is

$$\vec{v}_A=\vec{v}_B+\vec{a}.$$

Thus, the speed of A relative to C is

$$\vec{v}_{AC}=\vec{\nu}-\vec{v_A}=\vec{\nu}-\vec{v}_B-\vec{a}.$$