An asteroid is on collision course with Earth. As astronaut lands on the rock to

Question

An asteroid is on collision course with Earth. As astronaut lands on the rock to bury explosive charges that will blow the asteroid apart. Most of the small fragments will miss the Earth, and those that fall into the atmosphere will produce a meteor shower. The astronaut finds that the density of the spherical asteroid is equal to the average density of Earth. To ensure its pulverization, she incorporates into the explosives the rocket fuel and oxidizer intended for her return journey. What maximum radius can the asteroid have for her to be able to leave it entirely simply by jumping up? On Earth she can jump to a height of 0.500 m.

Explanation / Answer

on earth she can jump to a height of 0.5m. so let v be the maximum speed that she can produce by her legs. mv^2/2=mgh. so v=sqrt(2gh)=3.13(m/s). ---- density of the earth 5.519 g/cm3=5519(kg/m3). ----- so K=-GmM/r=-mGD(4/3 *pir^3)/r=-mGD4pir^2/3 K+mv^2/2=0. so GD4pi*r^2/3=v^2/2. so r=1781(m)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.