### Educational Content: Asteroid Impact on EarthMost geologists believe that the dinosaurs became extinct 65 million years ago when a large comet or asteroid struck the Earth. This event likely caused so much debris to be thrown into the atmosphere that it blocked out the sun for many months. To explore this concept further, let's consider a scenario:Suppose an asteroid with a diameter of **2.0 km** and a mass of **1.0 x 10¹³ kg** hits the Earth, which has a mass of **6.0 x 10²⁴ kg**, at an impact speed of **3.8 x 10⁴ m/s**.#### Exercise: Recoil Speed of Earth**Part A:** What is the Earth's recoil speed after such a collision? Assume a reference frame where the Earth is initially at rest.**Instructions:** Express your answer using the appropriate units.You are provided with a hint option to assist you in solving this problem. For calculations, input the value and units in the designated fields.This exercise helps understand the physics behind such catastrophic events and their implications on the Earth's motion. **Part B**What percentage is this of the earth’s speed around the sun? The earth orbits the sun at a distance of \(1.5 \times 10^{11} \text{ m}\).- **View Available Hint(s)**There is a text input box labeled \( v = \) where users can input a percentage, followed by the text "% of the earth's speed".Below the input box is a "Submit" button.

Given: Mass of asteroid, ma =1.0×1013 kg Mass of earth, me =6.0×1024 kg Impact or initial speed of asteroid, ua =3.8×104 m/s To determine: (A) recoil speed of earth after collision , the earth is initially rest. (B) percentage of the earth recoil speed with the speed around the sun.(A) Applying conservation of momentum to find recoil speed of earth. Conservation of momentum state that momentum before collision is equal to momentum after collision. after collision with earth the asteroid and earth become a single object, the total mass would be (ma + me) maua + meue = (ma + me)v (1) where v is speed after collision ma =Mass of asteroid, ma =1.0×1013 kg me = Mass of earth, me =6.0×1024 kg ua =Impact or initial speed of asteroid, ua =3.8×104 m/s and ue is initial speed of earth, ue =0 Putting all values in equation (1) (1.0×1013 kg)(3.8×104 m/s) = (1.0×1013 kg + 6.0×1024 kg)v v=(1.0×1013 kg)(3.8×104 m/s)(1.0×1013 kg + 6.0×1024 kg) v=6.33×10-8 m/s The recoil speed of earth after collision 6.33×10-8 m/s.(B) Speed of sun around sun is, Ve = 2πRT Where R is radius of earth , R=1.5×1011 m T is time period, Ve = 2π(1.5×1011 m)(365×24×3600 s) Ve = 29885.77 m/s The percentage of the earth recoil speed with the speed around the sun = vVe×100 =6.33×10-8 m/s29885.77 m/s×100 =2.118×10-10 %

Science

Physics

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 2.0 km and a mass of 1.0 × 103 kg hits the earth (6.0 × 1024 kg) with an impact speed of 3.8 × 10ª m/s. Part A What is the earth's recoil speed after such a collision? (Use a reference frame in which the earth was initially at rest.) Express your answer with the appropriate units. • View Available Hint(s) HÁ ? Value Units v =

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 2.0 km and a mass of 1.0 × 103 kg hits the earth (6.0 × 1024 kg) with an impact speed of 3.8 × 10ª m/s. Part A What is the earth's recoil speed after such a collision? (Use a reference frame in which the earth was initially at rest.) Express your answer with the appropriate units. • View Available Hint(s) HÁ ? Value Units v =

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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