1.

A rocket ship is 100m in length when measured before leaving the launchinng pad. when in flight a ground observer measures its length as 75m. the velocity of the rocket ship is

Answer»

We know, speed of light in VACCUM is 3 × 10^8 m/s . and speed of light decreases when it MOVES from rare medium to denser medium.

in CASE of rocket ship , use the formula,
\frac{l_1}{l_2}=\frac{1}{\sqrt{1-(<klux>V</klux>/c)^2}}
where , l_1 is the initial length of rocket ship.
c is the speed of light .
l_2 is the final length of rocket ship.
v is the speed of rocket ship.

100/75 = 1/√(1 - v²/c²)
4/3 = 1/√(1 - v²/c²)
squaring both sides,
16/9 = 1/(1 - v²/c²)
16(1 - v²/c²) = 9
16 - 9 = 16v²/c²
7c² = 16v²
TAKING square root both sides,
√7c/4 = v
v = (3 × 10^8 × √7)/4
= 1.98 × 10^8 m/s

hence, speed of rocket is 1.98 × 10^8 m/s


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