Question

As the earth rotates, what is the speed of a physics student in Miami, Florida, at latitude 26∘? Ignore the revolution of the earth around the sun. The radius of the earth is 6400 km. Express your answer with the appropriate units. vstudent = 416 ms

Answer 1

Answer:

$v =418 m/s$

Explanation:

given,

Radius of earth = 6400 Km

speed of a physics student in Miami, Florida, at latitude 26° = v

time period of rotation = 24 hour = 24 × 3600

                                                       = 86400 s

distance = speed × time

$v = \dfrac{distance}{time}$

$v = \dfrac{6400\times cos (26^0)\times 2 \pi }{86400}$

$v =0.41831 Km/s$

$v =418 m/s$

hence, the velocity of the student is equal to$v =418 m/s$

Answer 2

The speed(v) of a physics student in Miami, Florida is 418.32 m/sec

From the given information;

The radius of the physics student at latitude 26° can be computed as:

= 6400 cos(26°) × 1000 m

= 6400 (0.89879) × 1000 m

Assuming the circumference of the rotation  represents the distance which is:

= 2πr

= 2π (6400 (0.89879) × 1000 m)

Then, using the relation:

Speed = distance/ time

where;

• It takes 24 hours to make a day, in seconds, it will take:
• = 24 × 60 × 60
• = 86400 sec.

Then, the speed of the physics student in Miami is:

Speed = 2π 6400 (0.89879) × 1000 m /  86400 sec.

Speed = 418.32 m/sec

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