A person in an airplane has a mass of 74 kg and 6.6 MJ of gravitational potential energy. What is the altitude of the plane?

1 Answer
Mar 27, 2018

Answer:

The altitude is #"9100 m"# or #9.1xx10^3# #"km"#.

Explanation:

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"#