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 5.0 km and a mass of 2.5*10^14 kg hits the earth with an impact speed of 4.0*10^4 m/s.
Part A: What is the earth's recoil speed after such a collision? Assume that the mass of the earth is 5.98*10^24 kg. (Use a reference frame in which the earth was initially at rest.)

Part 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*10^11 m.

Answer 1

Answer:

A) 1.67 x 10 ⁻⁶ m/s

B)5.59 x $10^-^9$ %

Explanation:

A)

Given:

d = 5.0 km,

mₐ = 2.5 x $10^1^4$ kg

u₁ = 4.0 x 10⁴ m/s

$m_n$ = 5.98 x 10 ²⁴ kg

Solve using kinetic conserved energy

mₐ x u₁ + $m_n$  x u₂ = uₓ x (mₐ + $m_n$ )

(2.5 x $10^1^4$) (4.0 x 10⁴ )+ (5.98 x 10 ²⁴ )(0) = uₓ x (2.5 x $10^1^4$ + 5.98 x 10 ²⁴ )

uₓ = ( 2.5 x $10^1^4$ x 4.0 x 10⁴ ) / (2.5 x $10^1^4$ + 5.98 x 10 ²⁴ )    

uₓ = 1.67 x 10 ⁻⁶ m/s

B) Assuming earth radius as a R = 1.5 x 10 ¹¹ m

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

t = 31536000 s

D = 2 π R = 2 π( 1.5 x 10 ¹¹ )

D = 9.4247 x 10 ¹¹ m

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

u₂ =  29885.775 m/s

% = (  1.67 x 10 ⁻⁶ m/s ) / (29885.775 m/s) x 100

% = 5.59 x $10^-^9$ %