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A 1.0kg object is released from rest 500 km (?300 miles)
Chapter 13, Problem 33P(choose chapter or problem)
Problem 33P
A 1.0kg object is released from rest 500 km (≈300 miles) 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?
c. By what percentage is the flat-earth calculation in error?
Questions & Answers
QUESTION:
Problem 33P
A 1.0kg object is released from rest 500 km (≈300 miles) 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?
c. By what percentage is the flat-earth calculation in error?
ANSWER:
Part (a)
Step 1 of 4
An object is released from the height above the Earth. We are going to find the impact speed as it hits the ground.
The mass of the object \(m=1 \mathrm{~kg}\)
The initial height \(\mathrm{y}=500 \mathrm{~km}=5 \times 10^{5} \mathrm{~m}\)
The acceleration due to gravity \(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\)
The gravitational constant \(\mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}\)
The radius of the Earth \(\mathrm{R}=6.37 \times 10^{6} \mathrm{~m}\)
The mass of the Earth \(\mathrm{M}=5.98 \times 10^{24} \mathrm{~kg}\)
The initial speed of the object \(\mathrm{v}_{\mathrm{i}}=0\)
The final height \(y_{0}=0\)