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.

A. Suppose an asteroid with a diameter of 9.0 km and a mass of 1.0 x 10^15 kg hits the earth with an impact speed of 4.0 x 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 x 10^24 kg. (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? Assume that the orbit of the earth is a circle with the radius of 1.5 x 10^11 m.

A. uₓ = 6.68 x 10 ⁻⁶ m/s

B. % = 2.23 x 10 ⁻⁸ %

Explanation:

A.

d = 9.0 km, mₐ = 1.0 x 10¹⁵ kg, u₁ = 4.0 x 10⁴ m/s, mₙ = 5.98 x 10 ²⁴ kg

Solve using kinetic conserved energy

mₐ * u₁ + mₙ * u₂ = uₓ * (mₐ + mₙ)

1.0 x 10 ¹⁵ kg * 4.0 x 10⁴ m/s + 5.98 x 10 ²⁴ kg * 0 = uₓ * (5.98 x 10 ²⁴ kg + 1.0 x 10 ¹⁵ kg)

uₓ = (1.0 x 10 ¹⁵ kg * 4.0 x 10⁴ m/s) / (1.0 x 10 ¹⁵ + 5.98 x 10 ²⁴) kg

uₓ = 6.68 x 10 ⁻⁶ m/s

B.

Using a earth radius as a R = 1.5 x 10 ¹¹ m

t = 365 days * 24 hr / 1 day * 60 minute / 1 hr * 60s / 1 minute = 31536000 s

t = 31536000 s

D = 2 π * R = 2 π * 1.5 x 10 ¹¹ m

D = 9.4247 x 10 ¹¹ m

u₂ = D / t = 9.4247 x 10 ¹¹ m / 31536000 s

u₂ = 29885.775 m/s

% = (6.68 x 10 ⁻⁶ m/s) / (29885.775 m/s) * 100

% = 2.23 x 10 ⁻⁸ %