A newly-constructed spaceliner boasts a 105 m long and 65.0 m wide soccer field

Question

A newly-constructed spaceliner boasts a 105 m long and 65.0 m wide soccer field for the enjoyment of its international crew during extended missions. The long dimension of the soccer field is aligned along the ship's direction of flight. As the ship cruises by Earth, FIFA (Fédération Internationale de Football Association) officials on Earth measure the length of the field as 99.0 m and declare the field ineligible since it is shorter than the required 100 m. The captain protests that the discrepancy is due to length contraction. (a) How fast was the ship traveling according to the Earth-bound observers (as a decimal fraction of c)? (b) What is the width of the field according to the FIFA officials?

I have the answer to part B and I thought the answer to Part A was 0.33 c, however, it is telling me that is wrong. Can someone help me solve please?

Explanation / Answer

Length contraction

formula is L = L_0(sqrt(1- v^2/c^2))

length of the field measured from the boat frame(original) is 105 m,
length of the field measuered from earth's reference frame is 99 m, which is due to length contraction

from theory of relativity as the space liner boat moving nearly or slightly less than speed of light then there would be achangein length given by

   L= L_0(sqrt(1- v^2/c^2))
   99 = 105(sqrt(1- v^2/(3*10^8)^2))

   V =99959175.34 m/s => v = 99959175.34/3*10^8    = 0.3332 c

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