6. Three tugboats are using long steel cables to pull an aircraft carrier out of

Question

6. Three tugboats are using long steel cables to pull an aircraft carrier out of a repair dock. Each of these tugboats can exert a 150,000N pulling force. The tugboats are all side-by-side with 40m between them, with the one in the middle directly in front of the aircraft carrier. The middle tugboat is 200m from the aircraft carrier. All three cables are attached to a common point at the front of the aircraft carrier. It takes 15 minutes to get the aircraft carrier up to the desired speed of 10m/s.

Estimate the mass of the aircraft carrier.

Explanation / Answer

Angle made by other 2 tugboats with the central tugboat = tan-1(40/200) = tan-1(1/5) = 11.31

a = 10/(15x60) = 0.011 m/s2

Total force on Aircraft by tugboats = 150000 + 2x150000cos(11.31) = ma

=> 444174.133 = mx0.011

=> m = 40379466.6 kg

So mass of aircraft = 40379466.6 kg

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