Question

Q1.A rocket ship is 100m in length when measured before leaving the launching pad. when in flight a ground observer measure its length as 75m. what is the velocity of rocket ship?

Answer 1

Step-by-step explanation:

Let the original velocity of rocket be L and observed L'

L= 100 m

L' = 75 m

Using relative length formula,

$\begin{gathered}\frac{L}{L'}=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}\\\;\\\text{Where,c=velocity of light,\;\;v=velocity of rocket}\\\;\\\frac{100}{25}=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}\\\;\\\frac{4}{3}=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}\\\;\\\frac{3}{4}=\sqrt{1-\frac{v^{2}}{c^{2}}}\\\;\\\frac{9}{16}=1-\frac{v^{2}}{c^{2}}\\\;\\\frac{v^{2}}{c^{2}}=1-\frac{9}{16}\\\;\\\frac{v^{2}}{c^{2}}=\frac{16-9}{16}\\\;\\\frac{v^{2}}{c^{2}}=\frac{7}{16}\\\;\\v^{2}=\frac{7c^{2}}{16}\\\;\\v=\frac{\sqrt{7}c}{4}\\\;\\\end{gathered}$

Putting c = 3 × 10⁸ m/s

$</p><p>\begin{gathered}v=\frac{\sqrt{7}\times3\times10^{8}}{4}\\\;\\v=1.98\times10^{8}\:m/s\end{gathered}$