Question

A Foron cruiser moving directly toward a Reptulian scout ship fires a decoy toward the scout ship. Relative to the scout ship, the speed of the decoy is $\mathbf{0}\mathbf{.}\mathbf{980}\mathit{c}$and the speed of the Foron cruiser is $\mathbf{0}\mathbf{.}\mathbf{900}\mathit{c}$. What is the speed of the decoy relative to the cruiser?

Short answer

The speed of decoy relative to cruiser is $0.677c$.

Step-by-step solution

Identification of given data

The speed of decoy is $u=0.980c$

The speed of Foron is $v=0.900c$

The Foron is moving opposite to the decoy so speed of the Foron is taken opposite to the speed of decoy and we substitute speed of Foron in expression with negative sign.

Determination of speed of decoy relative to crusier

The speed of decoy relative to cruiser is given as:

$U=\frac{u+v}{1+\frac{u·v}{c^2}}$

Here, $c$ is the speed of light.

Substitute all the values in the above equation.

$$\begin{gathered} U=\frac{0.980c+\left(-0.900c\right)}{1+\frac{\left(0.980c\right)\left(-0.900c\right)}{c^2}} \\ U=0.677c \end{gathered}$$

Therefore, the speed of decoy relative to cruiser is $0.677c$.