Law of conservation of momentum question

[physics120]

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 1.0*10^13 kg hits the Earth with an impact speed of 4.0*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!

Thank-you

 

[Gib Z]

The data from your book is correct, but it appears that you forgot to multiply by 2pi! That number you have is the mean radius. If we assume the orbit is roughly circular, we multiply it by 2pi so we can get the circumference - THAT is the distance the Earth travels in a year.

 

[physics120]

I see! So I tried it again and found the circumference. Is it 2.2% for the percentage of the Earth's speed around the sun?

Thank-you, by the way!

 

[Gib Z]

Yup, that's correct! and no problem.