Frame S' moves relative to frame S at speed of 2.4 × $$10^8$$​ m/s in the direction of increasing x. An object is fired in frame S' at a speed of 1.8 × $$10^8$$​ m/s in the direction of increasing x'. The speed of the object according to an observer in frame S is

Correct option is C

​$$\begin{aligned}&\text{Given:} \\&\bullet \ \text{Frame } S' \text{ moves relative to frame } S \text{ at speed:} \quad v = 2.4 \times 10^8 \, m/s \\&\bullet \ \text{Object fired in frame } S' \text{ at speed:} \quad u' = 1.8 \times 10^8 \, m/s \\&\text{Concept:} \\&\text{ relativistic velocity addition formula:} \\&u = \frac{u' + v}{1 + \frac{u'v}{c^2}} \\[6pt]&\text{where } c = 3 \times 10^8 \, m/s \text{ is the speed of light.} \\[10pt]&u = \frac{1.8 \times 10^8 + 2.4 \times 10^8}{1 + \frac{(1.8 \times 10^8)(2.4 \times 10^8)}{(3 \times 10^8)^2}} = \frac{4.2 \times 10^8}{1 + 0.48} = \frac{4.2 \times 10^8}{1.48} = 2.84 \times 10^8 \, m/s\end{aligned}$$​​