+ 012 points | Previous Answers Tipler 11.P.091. My Notes • Ask Your Teacher A s

Question

+ 012 points | Previous Answers Tipler 11.P.091. My Notes • Ask Your Teacher A satellite is circling the moon (radius 1700 km) close to the surface at a speed v. A projectile is launched vertically up from the moon's surface at the same initial speed v. How high will the projectile rise? (Take m and M as the masses of the satellite and the moon, respectively.) 350 X Mm Use conservation of energy to establish a relationship between the height to which the projectile will rise and its initial speed. The application of Newton's second law will relate the orbital speed, which is equal to the initial speed of the projectile, to the mass and radius of the moon. ebook

Explanation / Answer

For circular path,

Fg = m a_c

G M m / R^2 = m v^2 / R

and v^2 = G M / R

{where M is mass of moon and R is radius of moon}

NOw applying energy conservation,

PEi + KEi = PEf + KEF

- G M m / R + m v^2 /2 = - G M m / r + 0

-G M m / R + G M / 2 R = - G M m / r

- G M m / 2 R = - G M m / r

so r = 2R

and height from surface = r - R = R

radius of moon = 1.74 x 10^6 m

Ans: h = 1.74 Mm

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