A body is projected away from the earth with a speed 3v, where v, is the escape velocity. The speed of the body at infinity will be

By the Law of conservation of energy (U+K)surface =(U+K)∞⇒−GMmR+12m3ve2=0+12mv12⇒−GMR+9ve22=12v12Since, ve2=2GMR⇒−ve22+9ve22=12v2⇒v2=8ve2⇒v=22ve