Did you think about this over christmas? i did (-: before christmas a 65kg student consumes 2500 cal each day and stays at the same weight. for three days in a row while visiting her parents she eats 3500 cal and, wanting to keep from gaining weight decides to "work off" the excess by jumping up and down at the christmas tree. with each jump she accelerates to a speed of 3.2 m/s before leaving the ground. a) how high will she jump each jump? b) how many jumps must she do to keep her weight? assume that the efficiency of the body in using energy is 25%. c) do you suggest that is a reasonable way for the student not to gain weight over christmas? d) possible enhancement: what other way/ways would you suggest for the student to keep her weight?

a)  Em = 332.8 J , b) # jump = 13, c)   It is reasonable since there are not too many jumps , d) lower the calories consumed

Explanation:

a) Let's use energy conservation

Initial. On the floor

             Em₀ = K = ½ m v²

Final. The highest point

             Emf = U = m g h

Energy is conserved

             Em₀ = Emf

             ½ m v² = m g h

             h = ½ v² / g

            h = ½ 3.2² /9.8

            h = 0.52 m

b) When he was at home he maintained his weight with 2500 cal / day. In his parents' house he consumes 3500 cal / day, the excess of calories is

            Q = 3500 -2500 = 1000cal / day

Let's reduce this value to the SI system

             Q = 1000 cal (4,184 J / 1 cal) = 4186 J / day

Now the energy in each jump is

               Em = K = ½ m v²

               Em = ½ 65 3.2²

               Em = 332.8 J

They indicate that the body can only use 25% of this energy

              Em effec = 0.25 332.8 J

              Em effec = 83.2 J

This is the energy that burns the body

Let's use a Proportion Rule (rule of three), if a jump spends 83.2J how much jump it needs to spend 1046 J

              # jump = 1046 J (1 jump / 83.2 J)

              # jump = 12.6 jumps / day

              # jump = 13  

c) It is reasonable since there are not too many jumps

d) That some days consume more vegetables to lower the calories consumed

because growing process had stoped after 4-5 year