Estimate the thickness of the Earth's atmosphere. From your chemistry class, you know that the most common speed of a nitrogen molecule is 650 m/s. The molecules' velocity is pointed along random directions, but some molecules head straight up; i.e. directly away from the Earth's center.
Physics · High School · Tue Nov 03 2020
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Answer
18.3km
Explanation:
The initial kinetic energy is 1/2 m v0^2. The initial potential energy, choosing to measure that relative to ground level, is zero.
At the top of the trajectory the kinetic energy is zero ( the particle stops to turn around) and the potential energy is m g h.
Conservation of total mechanical energy then implies
m g h = 1/2 m v0^2
So
h = v0^2/(2g)
= (600 m/s)^2/(2*9.81 m/s^2) = 18.3km