Most geologists believe that the dinosaurs became extinct 65 million years ago w

Question

Most geologists believe that the dinosaurs became extinct 65 million years ago when a large comet or asteroid struck the earth, throwing up so much dust that the sun was blocked out for a period of many months. Suppose an asteroid with a diameter of 9.0 km and a mass of 1.0 times 10^15 kg hits the earth with an impact speed of 4.5 times 10^4 m/s. What is the earth's recoil speed after such a collision? Assume that the mass of the earth is 5.98 middot 10^24 kg. (Use a reference frame in which the earth was initially at rest.) Express your answer to two significant figures and include the appropriate units. What percentage is this of the earth's speed around the sun? Assume that the orbit of the earth is a circle with the radius of 1.5 middot 10^11 m. Express your answer using two significant figures.

Explanation / Answer

here,

mass of asteroid , m1 = 1 * 10^15 kg

initial speed , u1 = 4.5 * 10^4 m/s

let the final speed of both be v1 and v2

using conservation of momentum

m1 * u1 = m1 * v1 + m2 * v2

1 * 10^15 * 4.5 * 10^4 = 1 * 10^15 * v1 + 5.98 * 10^24 * v2 ....(1)

using conservation of energy

0.5 * m1 * u1^2 = 0.5 * m1 * v1^2 + 0.5 * m2 * v2^2

1 * 10^15 * (4.5 * 10^4)^2 = 1 * 10^15 * v1^2 + 5.98 * 10^24 * v2^2 ....(2)

from (1) and (2)

v1 = - 45000 m/s

v2 = 1.5 * 10^-5 m/s

the earth recoil speed is 1.5 * 10^-5 m/s

b)

the earth's orbital speed , v = sqrt(G * Mass of sun /r)

v = sqrt( 6.67 * 10^-11 * 2 * 10^30 /(1.5 * 10^11))

v = 2.98 * 10^4 m/s

vrecoil/vorbital = (1.5 * 10^-5)/(2.98 * 10^4) * 100 = 5 * 10^-8 %

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.