Calculate the speed of an 7.8×104 kg airliner with a kinetic energy of 1.0 × 109 J.

Answer in units of m/s.

Use the definition of Kinetic Energy, (M/2)V^2, and solve for V.

A little algebraic manipulation should convince you that

V = sqrt[2*(K.E.)/M]

To calculate the speed of an airliner, we can use the formula:

Kinetic Energy = (1/2) * mass * velocity^2

Given:
Kinetic Energy = 1.0 × 10^9 J,
Mass = 7.8 × 10^4 kg

Rearranging the formula, we can solve for velocity:

velocity = square root( (2 * Kinetic Energy) / mass )

Now, plug in the given values:

velocity = square root( (2 * 1.0 × 10^9 J) / 7.8 × 10^4 kg )

Calculating this expression, we get:

velocity ≈ square root(25641025.641...)

Therefore, the speed of the airliner is approximately:

velocity ≈ 5064.2 m/s