Question

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.

Answer 1

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

Answer 2

Answer:

Explanation:

Given:

Velocity, v = 650 m/s

The initial kinetic energy and the initial potential energy, choosing to measure that relative to ground level, is zero.

Therefore, Using conservation of mechanical energy,

Potential energy = kinetic energy

M × g × h = 1/2 × M × v^2

h = (2 ×650^2)/9.8

= 86224.5 m

= 86.225 km.