Calculating the Earth's Recoil Speed After Asteroid Impact

[Dick Channy]

Homework Statement

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 2.0km and a mass of 1.3*10^13 kg hits the Earth with an impact speed of 4.2*10^4 m/s.

a) What is the Earth's recoil speed after such a collision? (Use a reference frame in which the Earth was initially at rest.)

b) What percentage is this of the Earth's speed around the sun?

Homework Equations

I used the law of conservation of momentum (Pf = Pi) This states that the total momentum after an interaction is equal to the total momentum before the interaction.

The Attempt at a Solution

a) Using Pf=Pi, I solved for the final velocity, which is the same for both the Earth and the asteroid, and got 668.896 m/s. (The final velocity is the Earth's recoil speed)

b) NOW for this part, I got from my textbook that the "earth's mean distance from sun (m) = 1.50*10^11 m. Also, I got that the Earth's period (years) = 1.00 years

Using these, I found the speed to be 4756.468798 m/s by converting years to seconds and dividing the two numbers (to get m/s)

Then,

(668.896m/s / 4756.4688798m/s) * 100% = 14%

Did I do this correctly? Did I use the correct numbers from my textbook to get the speed?

Please help!

[/B]

 

[collinsmark]

Hello @Dick Channy,

Welcome to Physics Forums!

Homework Statement

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 2.0km and a mass of 1.3*10^13 kg hits the Earth with an impact speed of 4.2*10^4 m/s.

a) What is the Earth's recoil speed after such a collision? (Use a reference frame in which the Earth was initially at rest.)

b) What percentage is this of the Earth's speed around the sun?

Homework Equations

I used the law of conservation of momentum (Pf = Pi) This states that the total momentum after an interaction is equal to the total momentum before the interaction.

The Attempt at a Solution

a) Using Pf=Pi, I solved for the final velocity, which is the same for both the Earth and the asteroid, and got 668.896 m/s. (The final velocity is the Earth's recoil speed)[/B]

I got something many orders of magnitude different.

Please show your work on that one. (Your approach of using conservation of momentum is correct though -- something must have gone wrong with the arithmetic.)

b) NOW for this part, I got from my textbook that the "earth's mean distance from sun (m) = 1.50*10^11 m. Also, I got that the Earth's period (years) = 1.00 years

Using these, I found the speed to be 4756.468798 m/s by converting years to seconds and dividing the two numbers (to get m/s)

Don't forget that the circumference of a circle is $2 \pi$ times the radius.