the sun sets, fully disappearing over the horizon as you lie on the beach, your eyes 10 cm above the sand. you immediately jump up, your eyes now 130 cm above the sand, and you can again see the top of the sun. If you count the number of seconds (=t) until the sun fully disappears again, you can estimate the radius of the Earth. Use radius of earth, 6.38*10^3 km, to calculate the time (t).

6.3 9.095...

To calculate the time (t) it takes for the sun to fully disappear again, we need to determine the change in distance between your eyes and the horizon.

First, let's convert the radius of the Earth from kilometers to centimeters to match the units used for the eye height above the sand.

Radius of Earth = 6.38 * 10^3 km = 6.38 * 10^8 cm

When you lie on the beach, your eyes are 10 cm above the sand, and you can see the sun disappear over the horizon.

When you jump up, your eyes are now at a height of 130 cm above the sand.

To calculate the change in distance, we subtract the eye height from the new eye height:

Change in distance = 130 cm - 10 cm = 120 cm

Now, we can calculate the angle subtended by this change in distance.

The angle subtended by an object at a certain distance is given by:

θ = arc tan (change in distance / distance to object)

In this case, the distance to the object is essentially the radius of the Earth.

θ = arc tan (120 cm / 6.38 * 10^8 cm)

Let's calculate the value of θ using this equation:

θ ≈ 1.887 * 10^-8 radians

Now, we need to calculate the time it takes for the sun to fully disappear again.

The sun moves across the sky at an angular speed of approximately 15° per hour (which is roughly 0.00417° per second).

The time it takes for the sun to move an angle θ is given by:

t = θ / angular speed

t = (1.887 * 10^-8 radians) / (0.00417°/s)

Let's calculate the value of t using this equation:

t ≈ 9.92 * 10^-7 seconds

Therefore, it takes approximately 9.92 * 10^-7 seconds for the sun to fully disappear again.