Beings on spherical asteroid Π have observed that a large rock is approaching their asteroid in a collision course.At 7514 km from the center of the asteroid,the rock has a speed of 136.0 m/s and later at 2823 km it has a speed of 392.0 m/s.Use energy conservation to find the mass of asteroid Π.You can neglect any effects due to the parent star of the asteroid.(G = 6.67 × 10^-11 N • m²/kg²) A) 4.582 × 10²¹ kg B) 9.164 × 10²⁷ kg C) 6.112 × 10²⁸ kg D) 4.582 × 10²⁰ kg

Question

Quizplus · Accepted Answer

Explanation:Using energy conservation, we have:$$K_i + U_i = K_f + U_f$$$$ \frac{1}{2}mv_i^2 - \frac{Gm_1m_2}{r_i} = \frac{1}{2}mv_f^2 - \frac{Gm_1m_2}{r_f}$$$$ \frac{1}{2}v_i^2 - \frac{G m_2}{r_i} = \frac{1}{2}v_f^2 - \frac{G m_2}{r_f}$$$$ \frac{1}{2}(136.0 	ext{ m/s})^2 - \frac{(6.67 	imes 10^{-11} 	ext{ N} \cdot 	ext{m}^2/	ext{kg}^2) m_2}{7514 	ext{ km}} = \frac{1}{2}(392.0 	ext{ m/s})^2 - \frac{(6.67 	imes 10^{-11} 	ext{ N} \cdot 	ext{m}^2/	ext{kg}^2) m_2}{2823 	ext{ km}}$$$$ m_2 = 4.582 	imes 10^{21} 	ext{ kg}$$

Beings on Spherical Asteroid Π Have Observed That a Large