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 %

answer; the correct answer is technician a; ///100%good luck

weight of the box is given as

here this is placed on the inclined of angle 42 degree

now this weight will have two components one is along the incline other is perpendicular to it

so here we need to apply a force parallel to incline opposite to its component of weight

so here the component of weight is given as

here we have

so it requires 75 n force to move it upwards