Question

a refueling aircraft transfers fuel to a fighter jet flying at the same speed. the refueling aircrafts mass is ten times the fighter jets mass. if the fighter jets kinetic energy is 0.15 gj (gigajoules), what is the refueling aircrafts kinetic energy? gj

Explanation:

Step1: Recall the formula for kinetic energy

The formula for kinetic energy is $KE = \frac{1}{2}mv^2$, where $m$ is the mass and $v$ is the velocity.

Step2: Analyze the given information

Let the mass of the fighter jet be $m_f$ and its velocity be $v$. The mass of the refueling aircraft $m_r = 10m_f$, and both have the same velocity $v$ (since they fly at the same speed).
The kinetic energy of the fighter jet $KE_f=\frac{1}{2}m_fv^2 = 0.15$ GJ.
The kinetic energy of the refueling aircraft $KE_r=\frac{1}{2}m_rv^2=\frac{1}{2}(10m_f)v^2$.

Step3: Relate the two kinetic energies

We can rewrite $KE_r$ as $10\times(\frac{1}{2}m_fv^2)$. Since $\frac{1}{2}m_fv^2 = KE_f = 0.15$ GJ, then $KE_r = 10\times KE_f$.

Step4: Calculate the kinetic energy of the refueling aircraft

Substitute $KE_f = 0.15$ GJ into the equation: $KE_r=10\times0.15 = 1.5$ GJ.

Answer:

1.5