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?

Question

Lily Adams · Accepted Answer

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

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"#

Olivia Askew · Answer

undefined To find the altitude of the plane, you can use the formula for gravitational potential energy:

Gravitational Potential Energy = mass × gravitational acceleration × height

Rearranging the formula to solve for height:

Height = Gravitational Potential Energy / (mass × gravitational acceleration)

Given:
- Mass (m) = 74 kg
- Gravitational Potential Energy (PE) = 6.6 MJ = 6.6 × 10^6 J
- Gravitational acceleration (g) = 9.8 m/s^2

Plug in the values:

Height = (6.6 × 10^6 J) / (74 kg × 9.8 m/s^2)

Calculate the height.