91影视

The velocity of the projectile, u=0.8 c

The velocity of Anna鈥檚 spacecraft, v=0.6 c

The expression for the Lorentz velocity transformation is given as follows.

$\mathbf{u}\mathbf{\text{'}}\mathbf{=}\frac{\mathbf{u}\mathbf{-}\mathbf{v}}{\mathbf{1}\mathbf{-}{\displaystyle \frac{\mathbf{uv}}{{\mathbf{c}}^{\mathbf{2}}}}}$ 鈥︹�� (i)

Here, u' is the velocity of the object in frame S' , u is the velocity of object in frame S , v is the velocity of frame S' relative to s and cis the speed of the light.

Calculate the speed of projectile relative to Anna鈥檚 spaceship.

Substitute 0.8c for u and 0.6c for v into equation (i).

$$\begin{gathered} u\text{'}=\frac{0.8c-0.6c}{1-{\displaystyle \frac{\left(0.8c\right)\left(0.6c\right)}{c^2}}} \\ u\text{'}=\frac{0.2c}{1-0.48} \\ u\text{'}=\frac{0.2c}{0.52} \\ u\text{'}=0.384c \end{gathered}$$

Hence the velocity of the projectile relative to Anna鈥檚 speed is 0.385c .

The Anna is moving with speed of the spaceship but Anna is stable with respect to the spaceship. The inertial observer will always see the same speed of light. The beam of the light moves with speed of the light relative to Anna.

Hence the speed of the light beam relative to Anna is c .