Newton's Theory of Gravity and impact speed

AI Thread Summary
The discussion centers on calculating the impact speed of a 1.0 kg object released from 500 km above Earth, with two scenarios: one considering Earth's curvature and the other assuming a flat Earth. The initial equation presented for impact speed is incorrect due to dimensional inconsistencies and misinterpretation of variables. Participants emphasize the importance of energy conservation principles in solving the problem. Clarification is sought regarding the flat Earth scenario, as its definition is ambiguous. The conversation highlights the need for accurate equations and understanding of gravitational dynamics.
Kalie
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A 1.0 kg object is released from rest 500 km above the earth.
A. What is its impact speed as it hits the ground? Ignore air resistance
B. What would the impact speed be if the Earth were flat?
I don't know how to start this.
I said that v=sqrt(2G*M_e*m/(R_e+300))= 1.33*10^9 but that is incorrect...I'm probably being stupid but please help
 
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Kalie said:
A 1.0 kg object is released from rest 500 km above the earth.
A. What is its impact speed as it hits the ground? Ignore air resistance
B. What would the impact speed be if the Earth were flat?
I don't know how to start this.
I said that v=sqrt(2G*M_e*m/(R_e+300))= 1.33*10^9 but that is incorrect...I'm probably being stupid but please help
You seem to recognize that this problem has something to do with energy conservation. With the reference of zero potential at infinity the object has potential energy at altitude, but also when it hits the ground. You have several dimensional inconsistencies in your equation. What is 300? Why are there both M_e and m on the right and no m on the left.?

I have no idea what part C is about. Flat how? A cube? A huge plane of mass? I have no idea.
 
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