The air temperature over a lake decreases linearly with height after sunset, since air cools faster than water. The mean molar mass of air is M=28.8×10−3kg/mol.

The questions are:
If the temperature at the surface is 28.00 ∘C and the temperature at a height of 260.0 m is 8.000 ∘C how long does it take sound to rise 260.0 m directly upward? [Hint: Use the equation v=sqrt(γRT/M) and integrate.]

At a height of 260.0 m, how far does sound travel horizontally in this same time interval?

To place a communications satellite into a geosynchronous orbit at an altitude of 22,240 mi above the surface of the earth, the satellite first is released from a space shuttle , which is in a circular orbit at an altitude of 185 mi, and then is propelled by an upper-stage booster to its final altitude. as the satellite passes through a, the booster's motor is fired to insert the satellite into an elliptic transfer orbit. the booster is again fired at b to insert the satellite into a geosynchronous orbit. knowing that the second firing increases the speed of the satellite by 4810ft/s, determine (a.) the speed of the satellite as it approaches b on the elliptic transfer orbit, (b.) the increase in speed resulting from the first firing at a.