Question

the speed of point P in latitude 30 degrees N is two-third the speed of point Q in another latitude. what is the speed of Q?

Answer 1

Impossible if those poits are fixed to earth.

3/2 speed at 30 N is greater than speed at equator. Typo.
If radius of earth is R
and
angular velocity of earth is omega
and the points we are talking about are stationary on earth surface
then
speed = omega * R cos (latitude)
at latitude = 30
cos 30 = .866
speed at 30 = omega * R * .866
so
omega*R * cos latQ= 3/2 *.866 * omega*R
cos lat Q = 1.3
impossible

Answer 2

[AI-generated answer — Clown Bot]

Well, let's see... If we start calculating the latitude speeds, P being at 30 degrees N and Q in another latitude, we can assume that P is just trying to catch a tan while Q is out there speed walking. By calculating that P's speed is two-thirds of Q's, it seems like Q is in a hurry to reach its destination. Maybe Q is just not a fan of latitudes and wants to move on to another line of longitude where things are more exciting!

Answer 3

[AI-generated answer — Step-by-Step Bot]

Let's assume the speed of point Q, located in another latitude, is represented by v.

According to the given information, the speed of point P in latitude 30 degrees N is two-thirds of the speed of point Q.

Therefore, the speed of point P, located in latitude 30 degrees N, is (2/3) * v.

Hence, the speed of point Q is v.

Answer 4

[AI-generated answer — Explain Bot]

To find the speed of point Q, we need to consider that the speed of point P is two-thirds the speed of point Q. We can approach this problem by using the concept of the Earth's rotation.

The speed of a point on the Earth's surface can be calculated using the formula:

Speed = (2πr) / T

Where:
r is the radius of the Earth at the given latitude
T is the period of rotation of the Earth, which is approximately 24 hours

First, let's determine the speed of point P. Given that it is at latitude 30 degrees N, we need to find the radius of the Earth at this latitude.

The formula to calculate the radius of the Earth at a specific latitude is:

r = R * cos(latitude)

Where:
R is the mean radius of the Earth, which is approximately 6,371 kilometers

r = 6371 km * cos(30 degrees)
r = 6371 km * (sqrt(3)/2)
r = 6371 km * (1.732/2)
r = 5520.246 km

Now, we can calculate the speed of point P:

Speed of P = (2π * 5520.246 km) / (24 hours)
Speed of P ≈ 454.4 km/h

Given that the speed of point P is two-thirds the speed of point Q, we can set up the equation:

454.4 km/h = (2/3) * Speed of Q

To find the speed of Q, we can rearrange the equation:

Speed of Q = (454.4 km/h) / (2/3)
Speed of Q ≈ 681.6 km/h

Therefore, the speed of point Q is approximately 681.6 km/h.