Chapter 48, Impacts on Earth Video Solutions, Pathways to Astronomy

Problem 1

What would be the radius of a meteoroid with a mass of $10^{6} \mathrm{kg}$ $(1000 \text { metric tons })$ if it were made of silicate rock with a density of $3 \mathrm{kg}$ per liter? If it were made of water ice with a density of $1 \mathrm{kg}$ per liter? Which would do more damage? Explain your reasoning.

Zachary Warner

Numerade Educator

02:00

Problem 2

Use the formula for the kinetic energy of a moving body to estimate the energy of impact of a $10^{6}-\mathrm{kg}(1000 \text { metric ton })$ object hitting the Earth at $30 \mathrm{km} /$ sec. Express your answer in kilotons of TNT, using the conversion that 1 kiloton is about $4 \times 10^{12}$ joules. Note: Be sure to convert kilometers/second to meters/second.

Zachary Warner

Numerade Educator

01:53

Problem 3

Suppose a major impact blasted out rock from a 100 -km diameter crater that was, on average, $1 \mathrm{km}$ deep. If all that material became dust that settled out evenly over the entire surface of the Earth, how thick a layer would it form?

Nicholas Majtenyi

Numerade Educator

03:33

Problem 4

There is about a 1 in 45,000 probability that the potentially hazardous asteroid named Apophis will impact Earth in 2036. Based on observations, the asteroid is estimated to have a mass of $2.1 \times 10^{10} \mathrm{kg},$ a diameter of $0.25 \mathrm{km},$ and a density of $2.6 \mathrm{kg} / \mathrm{L} .$ It has been estimated that its impact velocity would be $12.6 \mathrm{km} / \mathrm{sec} .$ If the mass may be uncertain by a factor of 3 and the impact velocity uncertain by a factor of $2,$ what is the range of predicted impact energy in joules?

Kai Chen

Princeton University

01:02

Problem 5

The "rule of thumb" ratio for crater diameter versus impactor diameter is $10: 1-$ the crater's diameter will be 10 times that of the impactor. If there is an uncertainty in the mass of Apophis of a factor of $3,$ what is the uncertainty in the asteroid's diameter? What range in crater size does this imply?

Narayan Hari

Numerade Educator

05:26

Problem 6

It is most likely that an asteroid will impact in an ocean rather than on land. Here is a simplified formula that gives the height of the wave $(h),$ in meters, at a distance of $1000 \mathrm{km}$ from the
impact site:
$$h=8 \times \sqrt{\left(\frac{D}{406}\right)^{3} \times\left(\frac{V}{20}\right)^{2} \times\left(\frac{\rho}{3}\right)},$$
where $D$ is the asteroid diameter in meters, $V$ is the velocity in $\mathrm{km} / \mathrm{sec},$ and $\rho$ is the asteroid density in $\mathrm{kg} / \mathrm{L}$. Calculate the expected tsunami height in meters at $1000 \mathrm{km}$ from the impact if Apophis happens to land in the middle of an ocean. How would you expect the tsunami height to vary with distance from the point of impact?

Keshav Singh

Numerade Educator