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Solved Problem on Kinematics
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The largest known star (until June 2019) is VY Canis Majoris in the constellation of Canis Major with an estimated diameter of 1,975,000,000 km. Making the (absurd) assumption that a commercial jet could fly close to the surface of the star at a constant speed of 990 km / h, how long would the jet take for a spin on the star, answer in years.


Problem data Problem diagram

Star with a diameter of 1,975,000,000 kilometers, and a plane flying near the surface at 990 kilometers per hour (highlighted).
figure 1

Solution

The distance that the airplane should travel is the circumference of the star, the length of a circle is given by
\[ C=2\pi r \]
where r is the radius of the circumference, the diameter of a circle being equal to 2r, the length of a circle can also be calculated by
\[ C=\pi D \]
where π = 3,14 the circumference of the star is
\[ C=3.14 \times 1975000000\\ C=6201500000\;\text{km} \]
As the plane speed is constant, we have that travel time is given by
\[ v=\frac{\Delta S}{\Delta t}\\ \Delta t=\frac{\Delta S}{v} \]
using the speed value given in the problem and the distance being the length of the circumference calculated above, we have
\[ \Delta t=\frac{6201500000}{990}\\ \Delta t=6264141\;\text{h} \]
Converting this value to years as it asks for the problem, we get
\[ \Delta t=6264141\;\cancel{\text{hours}} \times \frac{1\;\cancel{\text{day}}}{24\;\cancel{\text{hours}}} \times \frac{1\;\text {year}}{365\;\cancel{\text{days}}} \]
\[ \bbox[#FFCCCC,10px] {\Delta t=715\;\text{years}} \]

Note: for comparison, the Sun is 1,391,000 km in diameter, under the same conditions, the airplane would take "only" 184 days to go around the Sun.

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Fisicaexe - Physics Solved Problems by Elcio Brandani Mondadori is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .