Use the values RE = 6370 km = 3960 mi for the radius of the earthA gas gun is used to acce...

Use the values RE = 6370 km = 3960 mi for the radius of the earth

A gas gun is used to accelerate projectiles to high velocities for research on material properties. The projectile is held in place while gas is pumped into the tube to a high pressure P0 on the left and the tube is evacuated on the right. The projectile is then released and is accelerated by the expanding gas. Assume that the pressure p of the gas is related to the volume V it occupies by pVγ = constant, where γ is a constant. If friction can be neglected, show that the velocity of the projectile at the position, x is

where m is the mass of the projectile and A is the cross-sectional area of the tube.