8) On its maiden voyage in July 1952, the liner United States won the coveted Blue Ribbon for
the fastest crossing of the Atlantic from New York to Cornwall, U.K. The trip took 3 days 10
hours 40 min at an average speed of 34.5 knots (65.5 km/h). This was 10 h 2 min less than the
14-year-old record held by the Queen Mary. What was the average speed of the Queen Mary?

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Respuesta :

The relation of uniform motion allows to find the result for the speed of the Ship is;

  • The average speed of the Queen Mary is v = 16.22 m/s

Uniform movement.

Kinematics studies the movement of bodies, looking for relationships between position, velocity and acceleration, in the special case that acceleration is zero, it is called uniform motion.

             [tex]v= \frac{\Delta x}{t}[/tex]

where v is the speed, dx is the displacement, and t is the time.

They indicate that the average speed of the transatlantic was v= 65.5 km/h and a time of 3 days, 10 hours and 40 minutes was used.

International System of Measurements.

The unit systems are measurement systems that establish conventional to share measurements with precision and without errors, the most used is the International System of Measurements (SI), where the basic measurements are the meter and the second, let's reduce the magnitudes to these units .

      v= 65.5km/h ( [tex]\frac{1000 m}{1 km}[/tex] ) ( [tex]\frac{1 h}{3600 s}[/tex] ) = 18.19m/s

      t = t₁ +t₂ +t₃

      t₁= 3 days (24h/1day) (3600s/1h) = 259200s

      t₂ = 10h ( 3600s/1h) = 36000s

      t₃ = 40min ( 60s/1min) = 2400s

      t = 259,200 + 36,000 + 2,400 = 297,600 s

Let's find the distance traveled.

           Δx = vt

           Δx = 18.19  297600

           Δx = 5.41 10⁶ m

This distance is the same for both ships, they indicate that the time of the Queen Mary Ship is 10h 2 min more than the ocean liner.

      Δt = 10h (3600/1h)+ 2min (60s/1min) = 36120s

The total time of the Queen Mary is

      [tex]t_{Queen} = t_{transatlantic} + \Delta t[/tex]

      [tex]t_{Queen}[/tex] = 297600 + 36120

      t_{Queen} = 333720 s

We look for the average speed of the Queen MMary

     v= [tex]\frac{ \Delta x}{t}[/tex]

     v = [tex]\frac{5.41 \ 10^6 }{333720}[/tex]

     v = 16.22m/s

In conclusion using the uniform motion relation we can find the result for the speed of the ship is;

  • The average speed of the Queen Mary is v = 16.22 m/s

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