Question

I am trying to figure out how to solve the following: Calculate the speed of an 8.0 x 10(to the 4th)kg airliner with a kinetic energy of 1.1 x 10(to the 9th) J.

Answer 1

Calculate the speed of an $8.0 \times 10$ (to the 4th) kg airliner with a kinetic energy of $1.1 \times 10$ (to the 9th) J.

**Solution.**

$$m = 8 \cdot 10^{4} \, kg, \, E_k = 1.1 \cdot 10^{9} \, J;$$ $$v - ?$$

The kinetic energy of the airliner we calculate by formula:

$$E_k = \frac{m v^2}{2};$$

$E_k$ - the kinetic energy of the airliner;

$m$ - the mass of the airliner;

$v$ - the speed of the airliner.

$$2E_k = m v^2;$$ $$v^2 = \frac{2E_k}{m}.$$ $$v = \sqrt{\frac{2E_k}{m}}.$$ $$v = \sqrt{\frac{2 \cdot 1.1 \cdot 10^{9}}{8 \cdot 10^{4}}} = 165.83 \left(\frac{m}{s}\right).$$

**Answer:** The speed of the airliner is $v = 165.83 \, \frac{m}{s}$.