How much faster would a person be moving if they stood on top of a 20.4 m high building compared to the ground? Take the period to be one day, and the radius of the earth to be 6400 km. 0.00148 m/s 14.1 m/s 0.727 m/s 0.465 m/s

The speed of a person standing on the ground is determined by the rotation of the Earth. The formula for the speed of an object moving in a circle is v = ωr, where v is the speed, ω is the angular velocity, and r is the radius of the circle.

1. First, we need to convert the radius of the Earth from kilometers to meters because the height of the building is given in meters. So, r1 = 6400 km = 6400 * 1000 m = 6,400,000 m.

2. The angular velocity (ω) of the Earth is the same for everyone on it, regardless of their position. It's calculated by dividing 2π (the number of radians in a full circle) by the period (T), which is one day or 246060 = 86,400 seconds. So, ω = 2π / 86,400 s = 7.27 * 10^-5 rad/s.

3. Now we can calculate the speed of a person standing on the ground using the formula v = ωr. So, v1 = ω * r1 = 7.27 * 10^-5 rad/s * 6,400,000 m = 465.28 m/s.

4. To find the speed of a person standing on top of the building, we need to add the height of the building to the radius of the Earth. So, r2 = r1 + 20.4 m = 6,400,020.4 m.

5. Now we can calculate the speed of a person standing on top of the building using the formula v = ωr. So, v2 = ω * r2 = 7.27 * 10^-5 rad/s * 6,400,020.4 m = 465.29 m/s.

6. To find out how much faster a person would be moving if they stood on top of the building compared to the ground, we subtract the speed of the person on the ground from the speed of the person on the building. So, Δv = v2 - v1 = 465.29 m/s - 465.28 m/s = 0.01 m/s.

So, a person would be moving 0.01 m/s faster if they stood on top of a 20.4 m high building compared to the ground. This is a very small difference, so in practical terms, the person's speed would be essentially the same in either location.