1. the 05.30 flight to malaga takes off with a mass, including fuel, passengers, luggage and crew, of
300,000kg. the gravitational field strength is 10n/kg.
a) the plane climbs to an altitude of 1200m. if the runway was at an altitude of 220m, how much
gravitational potential energy has it gained in kilojoules?
b) by lunchtime, the plane has used up some fuel and is now 50,000kg lighter. how much gravitational
potential energy has the plane lost? (it's still at 1200m.)

Newton's law of cooling states that the rate of change in the temperature t(t) of a body is proportional to the difference between the temperature of the medium m(t) and the temperature of the body. that is, startfraction dt over dt endfraction equals upper k left bracket upper m left parenthesis t right parenthesis minus upper t left parenthesis t right parenthesis right bracket , where k is a constant. let kequals0.04 left parenthesis min right parenthesis superscript negative 1 and the temperature of the medium be constant, m(t) font size decreased by 3 equivalent font size decreased by 3 294 kelvins. if the body is initially at 369 kelvins, use euler's method with hequals0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes.