Problem 5.58 About 65 million years ago a 10-km-diameter 2×1015kg meteorite trav

Question

Problem 5.58

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.

Part A

Determine the speed Earth gained as a result of this impact. The mass of Earth is 5.98×1024kg.

Express your answer to two significant figures and include the appropriate units.

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Significant Figures Feedback: Your answer 3.34106ms was either rounded differently or used a different number of significant figures than required for this part.

Part B

Find the average force that the meteorite exerted on Earth during the collision. Assume the stopping distance to be 1700 m .

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Here,

speed of meteriot , u1 = 10 km/s

u1 = 10000 m/s

mass ,m1 = 2 *10^15 Kg

part A)

let the velocity of earth after the collision is v1

mass of earth , m1 = 5.98 *10^24 kg

Using conservation of momentum

(m1+ m2) * v1 = m1 * u1

(5.98 *10^24 + 2 *10^15) * v1 =2 *10^15 * 10 * 10^3

v1 = 3.4 *10^-6 m/s

the speed of earth after the collision is 3.4 *10^-6 m/s

part B)

let the force exerted by the meteotrire is F

as the earth also exerts the same force on the meteotite

Using Work energy theorum

F * 1700 = 0.5 * 2 *10^15 * 10000^2

F = 5.88 *10^15 N

the average force that the meteorite exerted on Earth during the collision is 5.88 *10^15 N

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