A rocket ascends vertically through the atmosphere with a velocity that can be

assumed to increase linearly with altitude from zero at sea level to $1800$ m$/$s at an

altitude of $30,000$ m$.$ If the surface of this rocket is assumed to be adiabatic, esti$-$

mate the variation of the skin temperature with altitude at a point on the surface of

the rocket a distance of $3$ m from the nose of the rocket. Use the flat plate equations

given in this chapter and assume that at the distance from the nose considered, the

Mach number, and temperature outside the boundary layer are the same as those

in the freestream ahead of the rocket.