An \( 80000-\mathrm{kg} \) airliner is flying at \( 900 \mathrm{~km} / \mathrm{h} \) at a height of 10.0 km . What is its total energy (kinetic + potential) if the total was 0 when the airliner was at rest on the ground? 1) 250 MJ 2) 478 MJ 3) 773 MJ 4) 10300 MJ 5) 12500 MJ

To find the total energy of the airliner, we need to calculate both its kinetic energy (KE) and potential energy (PE). The kinetic energy can be calculated using the formula: \[ KE = \frac{1}{2}mv^2 \] where \( m = 80000 \, \text{kg} \) and \( v = 900 \, \text{km/h} = \frac{900 \times 1000}{3600} = 250 \, \text{m/s} \). So, \[ KE = \frac{1}{2} \times 80000 \, \text{kg} \times (250 \, \text{m/s})^2 = \frac{1}{2} \times 80000 \times 62500 = 2500000000 \, \text{J} = 2500 \, \text{MJ} \] For potential energy, we use the formula: \[ PE = mgh \] where \( g \) (acceleration due to gravity) is approximately \( 9.81 \, \text{m/s}^2 \), and \( h = 10.0 \, \text{km} = 10000 \, \text{m} \). So, \[ PE = 80000 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 10000 \, \text{m} = 7848000000 \, \text{J} = 7848 \, \text{MJ} \] Now, we can find the total energy by adding KE and PE: \[ Total \, Energy = KE + PE = 2500 \, \text{MJ} + 7848 \, \text{MJ} = 10348 \, \text{MJ} \] The closest choice to our answer is: **4) 10300 MJ**.