About 65 million years ago a 10-km-diameter 2×1015kg meteorite traveling at abou

Question

About 65 million years ago a 10-km-diameter 2×1015kg meteorite traveling at about 10 km/s crashed into what is now the Gulf of Mexico. The impact produced a cloud of debris that darkened Earth and led to the extinction of the dinosaurs.Determine the speed Earth gained as a result of this impact. The mass of Earth is 5.98×1024kg.Find the average force that the meteorite exerted on Earth during the collision. Assume the stopping distance to be 1750 m . Please include all work and fomulas to receive full credit. Units are m/s

Explanation / Answer

Here ,

mass of meterorite , m = 2 *10^15 Kg

mass of earth , M = 5.98 *10^24 Kg

inital speed , u = 10 km/s

u = 10000 m/s

Now , let the final speed gained is v m/s

Using conservation of momentum

(m + M) * v = m * u

(2 *10^15 + 5.98 *10^24 ) * v = 2 *10^15 * 10000

v = 3.344 *10^-6 m /s

the speed gained by earth is 3.344 *10^-6 m /s

let the acceleration is a

Using third euqation of motion

0 - 10000^2 = 2 * a * 1750

a = - 28571 m/s^2

force applied = m * a

force applied = 2 *10^15 * - 28571

force applied = 5.714 *10^19 N

as the force on earth = force on meteroid

the average force that the meteorite exerted on Earth during the collision is 5.714 *10^19 N

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