The formula for gravitational potential energy is:
#PE_"grav"=("m")("g")("h")#,
where:
#"PE"_"grav"# is gravitational potential energy in Joules #("J")#, #m# is mass in kg #("74 kg")#, #g# is acceleration due to gravity #("9.8 m/s"^2")#, and #h# is height (altitude) in meters.
You need to convert #"6.6 MJ"# to #"J"#.
#"1 J"##=##1xx"10"^(-6)"MJ"#
#6.6"MJ"xx(1"J")/(1xx10^(-6)"MJ")="6600000 J"=6.6xx10^6# #"J"#
Solution
Rearrange the formula to isolate #h#. Plug in the known values and solve.
#h=(PE_"grav")/(m*g)#
#h=(6.6xx10^6"J")/(74"kg"*"9.8m/s"^2)="9100 m"=9.1xx"10"^3" km"# (rounded to two significant figures)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To see how the units cancel, refer to the following information.
#"1 J = 1 N"*"m"#
#1 N*m=(1 kg*m/s^2*m)#
#h=(6.6xx10^6(color(red)cancel(color(black)("kg")))(color(red)cancel(color(black)("m"))/color(red)cancel(color(black)("s"^2)))("m"))/(74color(red)cancel(color(black)("kg"))*9.8color(red)cancel(color(black)("m"))/color(red)cancel(color(black)("s"^2")))##=##"9100 m"=9.1xx"10"^3" km"#
