In the past,Earth has been hit by many asteroids,some very large.Suppose one such asteroid approached Earth so that when it was very far away it was traveling at 6500 m/s along a line that would miss the center of Earth by 8,500,000 m.Because of the gravitational attraction of Earth,it departed from this straight line and curved towards Earth,colliding with it.What was the speed of this asteroid when it hit Earth if we ignore the effect of the sun? The mass of Earth is 5.97 × 10²⁴ kg,its radius is 6.38 × 10⁶ m,and G = 6.67 × 10^-11 N ∙ m²/kg².

Question

Quizplus · Accepted Answer

Using conservation of energy, we can find the velocity of the asteroid just before it hits the Earth. At very far distances, the gravitational potential energy is zero and the kinetic energy is 
KE = (1/2)mv², where m is the mass of the asteroid and v is its velocity. As the asteroid approaches the Earth, potential energy is converted to kinetic energy. At the moment of impact, all the potential energy has been converted to kinetic energy. This means that 
(1/2)mv² = GMm/R, 
where M is the mass of the Earth, R is its radius, and G is the gravitational constant. Solving for v, we get 
v = sqrt(2GM/R) = sqrt(2*6.67×10⁻¹¹*5.97×10²⁴/6.38×10⁶) = 12,900 m/s. 
Therefore, the answer is B.

In the Past,Earth Has Been Hit by Many Asteroids,some Very