Question

A comet is traveling through space with a speed of 3.80 ✕ 10⁴ m/s when it collides with an asteroid that was at rest. The comet and the asteroid stick together during the collision process. The mass of the comet is 1.75 ✕ 10¹⁴ kg, and the mass of the asteroid is 7.05 ✕ 10²⁰ kg.

(a) What is the magnitude of the momentum of the system's center of mass before the collision?
  
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. kg · m/s

(b) What is the magnitude of the momentum of the system's center of mass after the collision?
  

Answer 1

(a) Mass of comet m = 1.75 x 10^(14) kg;

Mass of asteroid M = 7.05 x 10^(20) kg;

Speed of commet before before collision v = 3.8 x 10^4 m/s;

speed of asteroid before collision V = 0 m/s;

let the speed of system after collision is = v';

(a) Find momentum of the system before collision;

Momentum of comet before collision Pc = mv = 1.75 x 10^(14) x 3.8 x 10^4 = 6.65 x 10^(18) kg m/s

Momentum of asteroid before collision Pa = MV = 7.05 x 10^(20) x 0 = 0 kg m/s

momentum of the system before collision P = Pc + Pa;

P = 6.65 x 10^(18) kg m/s

(b) momentum of the system's center of mass after the collision;

Apply conservation of momentum;

momentum of the system before collision = momentum of the system after collision

6.65 x 10^(18) = momentum of the system after collision

P' = 6.65 x 10^(18) kg m/s