USAAAO 2024, I кръг — Задача 7

USAAAO 2024 - First Round · 10 февруари 2024 г.

Problem writers

Wesley Andrade, Abhay Bestrapalli, Austin Chen, Justin Chen, Ved Gund, Hagan Hensley, Sandesh Kalantre, Evan Kim, David Lee, Joe McCarty, Arjun Patel, Sahil Pontula, Tara Rezaei, Raul Teixeira, Leo Yao, David Zhang

Условие

Arjun launches a 50 kg rocket with speed 10,405 m/s from the surface of the Earth and redirects it into a stable elliptical orbit. Upon analysis, he finds the area of the orbit to $1.438 \times 10^{15}$ m$^2$. What is the approximate distance between the periapsis of the orbit and the center of the Earth? Assume no energy was lost in the redirection of the rocket into its new orbit.

(a) 10000 km

(b) 5000 km

(c) 2000 km

(d) 39000 km

(e) 15000 km

Отговори

Решение

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Оригинал в Архива: usaaao_first_exam_2024-3.pdf · официални решения: usaaao_first_exam_2024_solutions-1.pdf