One way to attack a satellite in Earth orbit is to launch a swarm of pellets in
ID: 2252602 • Letter: O
Question
One way to attack a satellite in Earth orbit is to launch a swarm of pellets in the same orbit as the satellite but in the opposite direction. Suppose a satellite in a circular orbit 730 km above Earth's surface collides with a pellet having mass 7.5 g. (a) What is the kinetic energy of the pellet in the reference frame of the satellite just before the collision? (b) What is the ratio of this kinetic energy to the kinetic energy of a 7.5 g bullet from a modern army rifle with a muzzle speed of 810 m/s?
One way to attack a satellite in Earth orbit is to launch a swarm of pellets in the same orbit as the satellite but in the opposite direction. Suppose a satellite in a circular orbit 730 km above Earth's surface collides with a pellet having mass 7.5 g. (a) What is the kinetic energy of the pellet in the reference frame of the satellite just before the collision? (b) What is the ratio of this kinetic energy to the kinetic energy of a 7.5 g bullet from a modern army rifle with a muzzle speed of 810 m/s?
Explanation / Answer
(a) Taking the radius of earth to be 6370 km
r = 6370 + 730 km = 7.1 * 10^6m.
v = 2 * sqrt(9.8 * 7.1 * 10^6) m/s = 16682.9 m/s
KE = 0.5 * 0.0075 * 16682.9^2 J
= 1043696 J = 1043.69 kJ
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(b)The bullet speed is given = 810m/s
KE = 0.5 * 0.0075 * 810^2 J = 2460 J
The ratio = 1043696 / 2460 = 424 : 1
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