Question

Kate is the captain of a large cruise ship. As she
drives the ship, she sits 50 meters above the sea.
Paul is the captain of a boat. He sits 15 meters
above the sea. If the radius of the earth is
6,371,000 meters, how much further can Kate see
across the horizon than Paul?

Answer 1

Kate can see across the horizon by 3.33 times further than Paul.

What is the shape of the horizon?

The assumed shape of the horizon shows that it forms a cone shape. The volume of the cone can be used to determine how far they can see.

The volume of the cone $\mathbf{ V=\pi r \dfrac{h }{3}}$

For Kate:

• Height (h) = 50 m
• Radius (r) = 6,371,000 m

$\mathbf{ V=\pi r \dfrac{h }{3}}$

$\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{50 }{3}}$

V = 2.12526863 × 10¹⁵ m³

For Paul

• Height (h) = 15 m
• Radius (r) = 6,371,000 m

$\mathbf{ V=\pi r \dfrac{h }{3}}$

$\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{15 }{3}}$

V = 6.3758059 × 10¹⁴ m³

To determine how much further can kate see across the horizon than Paul, we have:

= Volume of Kate/Volume of Paul

= 2.12526863 × 10¹⁵ m³/6.3758059 × 10¹⁴ m³

= 3.33 times further.

Learn more about Plane shapes here:

https://brainly.com/question/4504103

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