o00 AT&T; LTE 6:44 PM 22% D Done a edugen.wileyplus.com C Chapter 13, Problem 04

Question

o00 AT&T; LTE 6:44 PM 22% D Done a edugen.wileyplus.com C Chapter 13, Problem 040 A projectile is shot directly away from Earth's surface. Neglect the rotation of the Earth. What multiple of Earth's radius R, gives the radial distance (from the Earth's center) the projectile reaches if (a) its initial htospeed is 0.283 of the escape speed from Earth and (b) its initial kinetic energy is 0.283 of the kinetic energy required to escape Earth? (Give your answers as unitless numbers.) (c) What is the least initial ?rnhim | mechanical energy required at launch if the projectile is to escape Earth?

Explanation / Answer

(A) v_escape = v0 = sqrt(2 G M / Re)

Applying energy conservation,

PEi + KEi = PEf+ KEf

- G M m / Re + m (0.283 v0)^2 /2 = - G M m / r + 0

- G M / Re + 0.08 G M / Re = - G M / r

r = 1.087 Re

Ans: 1.087 no unit

(B) KE = G M m / Re

KEi = 0.283 G M m / Re

So, - G M m / Re + 0.283 G M m / Re = - G M m / r + 0

r = 1.395 Re

Ans: 1.394 no units

(C) inital mechanical energy = 0

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