A projectile is fired straight upward from the Earth\'s surface at the South Pol

Question

A projectile is fired straight upward from the Earth's surface at the South Pole with an initial speed equal to one third the escape speed. (The radius of the Earth is 6.38 106 m.) (a) Ignoring air resistance, determine how far from the center of the Earth the projectile travels before stopping momentarily. 7.18*10e6 Incorrect: Your answer is incorrect. Your response is off by a multiple of ten. m (b) What is the altitude of the projectile at this instant? 8.0*10e5 Incorrect: Your answer is incorrect. Your response is off by a multiple of ten. m

Explanation / Answer

given

initial speed, v = vesc/3

vesc = 11,200 m/s

hence

v = 3733.33 m/s

a. let final distance from the center of the earth be r

then

-GM/R + 0.5v^2 = -GM/r

also, M = 5.972*10^24 kg

R = 6.38*10^6 m

hence

r = 7.1816*10^6 m

b. altitude of projectile = r - R = 0.8016*10^6 m

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