- #1

TRB8985

- 74

- 15

- Homework Statement
- The gravitational pull of the Earth on an object is inversely proportional to the square of the distance of the object from the center of the Earth. At the Earth’s surface, this force is equal to the object’s normal weight, mg, where 𝑔 = 9.8 𝑚/𝑠^2 , and at large distances, the force is zero.

If a 20,000 kg asteroid falls to Earth from a very great distance away, what will be its minimum speed as it strikes the Earth’s surface, and how much kinetic energy will it impart to our planet? You can ignore the effects of the Earth’s atmosphere.

- Relevant Equations
- Kinetic energy imparted to planet = m_asteroid * g * radius_Earth

Good morning,

I've completed the problem provided above and have verified my answers are correct, but I'm running into a strange situation when it comes to the solution's answer for the kinetic energy portion.

For the kinetic energy imparted to the planet, we're taking 20,000 kg * 9.8 m/s² * 6.371E6 m. This completely matches the solution's answer.

I'm aware that there's one significant figure in 20,000, two in 9.8, and 4 in 6.371E6. My understanding is that when multiplying these values together, the result should be reported using the lowest number of significant figures in these three values - so just one, 1E12 J.

The official solution for this problem reports three, however - 1.25E12 J.

Am I making a mistake in my reporting of the answer? Or is the provided solution using the incorrect number of significant figures here?

Thank you!

I've completed the problem provided above and have verified my answers are correct, but I'm running into a strange situation when it comes to the solution's answer for the kinetic energy portion.

For the kinetic energy imparted to the planet, we're taking 20,000 kg * 9.8 m/s² * 6.371E6 m. This completely matches the solution's answer.

I'm aware that there's one significant figure in 20,000, two in 9.8, and 4 in 6.371E6. My understanding is that when multiplying these values together, the result should be reported using the lowest number of significant figures in these three values - so just one, 1E12 J.

The official solution for this problem reports three, however - 1.25E12 J.

Am I making a mistake in my reporting of the answer? Or is the provided solution using the incorrect number of significant figures here?

Thank you!