Question

Newly sprouted sunflowers can grow at a rate of 0.75 cm per day. One sunflower is left on Earth, and another one is placed on a spacecraft traveling away from Earth at a speed of 0.94c. How tall is the sunflower on the spacecraft (as measure by someone on the spacecraft) when a person on Earth says theirs is 4.5 cm tall? How tall is the sunflower on the spacecraft (as measured by the person on Earth)? (Note: The direction of sunflower growth is the same as the direction that the spaceship is moving)

Answer 1

height grown by sunflower on earth everyday = 0.75 cm

total height grown = 4.5 cm

therefore, number of days passed = 4.5/.75 days = 6 days (on earth).

therefore time passed in space craft (proper time)=

=

= 2.047 days

therefore the height of flower as measured by someone on spacecraft (proper length) = 2.047 * 0.75 = 1.535 cm

the height of flower measured by person on earth = 4.5 cm

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