onsequennis then found I., Ic-rting ξ(33)lhe escape velocityof the escape velocity neglects the effect of air resistance, so theincluding the effect of air resistance) is somewhat higher. On the other6.9 mils, or 11.1 km/sThe numerical value of , is approximatelyThe preceding calculation of the escape vetance above sea level before being launched. Both gravitational and frictionalereby reduced; air resistance, in particular, diminishes quite rapidly with increasingeep in mind also that it may well be impractical to impart too large aninstantaneously; space vehicles, for instance, receive their initial accelerationpe velocity can be significantly reduced if the body is transportedconsiderable disforces are thinitial velocityduring a period of a few minutes.PROBLEMSConsider a tank used in certain hydrodynamic experiments. After one experiment thetank contains 200 L of a dye solution with a concentration of 1 g/L. To prepare forthe next experiment, the tank is to be rinsed with fresh water flowing in at a rate of2 L/min, the well-stirred solution flowing out at the same rate. Find the time that willelapse before the concentration of dye inthe tank reaches 1% of its original value.2. A tank initially contains 120 L of pure water. A mixture containing a concentration ofγ g/L of salt enters the tank at a rate of 2 L/min, and the well-stirred mixture leaves thetank at the same rate. Find an expression in terms of y for the amount of salt in the tankat any time t. Also find the limiting amount of salt in the tank as t-oo3. A tank originally contains 100 gal of fresh water. Then water containinglb of salt pergallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave atthe same rate. After 10 min the process is stopped, and fresh water is poured into the tankat a rate of 2 gal/min, with the mixture again leaving at the same rate. Fsalt in the tank at the end of an additional 10 min.mou4. A tank with a capacity of 500 gal originally contains 200 gal of wlbalthin solution. Water containing 1 lb of salt per gallon entering athe mixture is allowed to flow out of the tankof salt in the tank at any time prior to the inFind the concentration (in pounds per gallof overflowing. Compare this concentratithe tank had infinite capacitythhe5. A tank contains 100 gal of water and S