If the swimmer could cross the English Channel (32km) maintaining the same
velocity as for the first 50 m in the pool, how long would it take? (Actual times
are around 15 hours.) Answer: 4.3h.

Respuesta :

Maintaining the same velocity, the time taken by the swimmer to swim the first 50m across the English Channel is 4.3hrs.

This question is incomplete, the complete question is;

If the swimmer could cross the English Channel (32km) maintaining the same  velocity as for the first 50 m in the pool, how long would it take?

For the first 50m in the pool, the average velocity was 2.08 m/s

(Actual times are around 15 hours.)

Given the data in the question;

  • Distance of the English Channel; [tex]d_1 = 32km = 32000m[/tex]
  • Distance swam by the swimmer; [tex]d_2 = 50m[/tex]
  • Average velocity of swimmer; [tex]\delta v = 2.08 m/s[/tex]

We calculate the time taken by the swimmer for the first [tex]50m[/tex] in the pool.

We know that; Speed is distance travelled by a particle per unit time.

Speed = Distance / Time

Hence, Time = Distance / Speed

[tex]t =\frac{ \delta d }{ \delta v}[/tex]

Here, [tex]\delta d[/tex] is change in distance, [tex]\delta v[/tex] is the average velocity and t is time taken.

Hence,

[tex]t = \frac{d_1 - d_2}{\delta v }[/tex]

We substitute our given values into the equation;

[tex]t = \frac{32000m - 50m}{2.08 m/s}[/tex]

[tex]t = \frac{31950m}{2.08m/s}[/tex]

[tex]t = 15360.5769 s[/tex]

We convert to seconds to hours

[tex]t = \frac{15360.5769}{(60*60)} hrs[/tex]

[tex]t = 4.26 = 4.3 hrs[/tex]

Therefore, maintaining the same velocity, the time taken by the swimmer to swim the first 50m across the English Channel is 4.3hrs.

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