14.1.10∗. a. According to observations from the Earth, the velocities of two spacecraft flying toward each other are $v$ and $u$. Show that the relative velocity of one spacecraft as observed from the other is determined by the formula:$$v_1 = \frac{v + u}{1 + vu/c^2}$$b. According to observations from the Earth, a spacecraft is receding from it at a velocity $v$. A probe is launched from the spacecraft in the direction of its motion. According to observations from the spacecraft, the probe moves relative to it at a velocity $u$. Prove that the velocity of the probe's recession from the Earth, as observed from the Earth, is equal to:$$(v + u)/(1 + vu/c^2)$$In solving these problems, utilize the constancy of the speed of light in different reference frames.
