ElectricPavlov

Pretty rampant parenthetical lack on this site ! 

GPE = mgh

39200  = 200 kg  * 9.81 m/sec^2  * h        Solve for 'h'

39200/(200*9.81) = h meters       

Since there is a 1/2 sphere at each end, this is a complete sphere

Sphere volume     v =4/3 pi r^3  =   4/3 pi (5)^3 = 500pi/3  cm^3

The cylinder volume =  pi r^2 h = pi 5^2 (30) = 750 pi

Added together      750 pi + 500/3 pi = (2750 pi) /3    cm^3                   not rounded.

                                                               ~2880 cm^3    rounded

\(\int_{0}^{40}\)c(t) dt      is the total calories burned during the workout......

\(\int_{0}^{10}\) t-.05t^2+15  dt     +     \(\int_{10}^{30}\) 20   dt   +       \(\int_{30}^{40}\)3t-.05t^2-25  dt     = total calories burned

First part:   1/2 t^2 - .05/3 t^3 + 15 t       From 0 to 10 =    50 - 16.67 + 150  =183.33 cal

Second part:   20 t      from 10 to 30 =      600 - 200 = 400 cal

Third part:   Think you can do this one?

It has BOTH as I calculated for ya ....

School A   1v + 10b = 300

School B    4v + 5b = 185     Multiply second equation by -2 and add to equation 1 to get

              -7v = -70

                  v = 10

Sustitute this value in for v in either one of the equations to find b

10 + 10b = 300

10 b = 290

b = 29

KE = 1/2 mv^2  =  1/2  20  5^2 = 250j     remember to put in ALL of the values for the equation   and   v is v^2    

AND

GPE = mgh = 20   9.81    2  = 392.4 j

Close....   It does NOT have GPE since it is not elevated above the ground

It DOES have Kinetic Enegy because it is rolling  1/2  m v^2  =   1/2  2 kg  (10 m/s)^2 = 100 j