Calculate the speed of an 8.0 × 104 kg airliner with a kinetic energy of 1.1 × 109 J.
To calculate the speed of the airliner, we can use the equation for kinetic energy:
Kinetic energy = (1/2) * mass * speed^2
Given:
Kinetic energy = 1.1 × 10^9 J
Mass = 8.0 × 10^4 kg
We can rearrange the equation to solve for speed:
Speed^2 = (2 * Kinetic energy) / mass
Speed^2 = (2 * 1.1 × 10^9 J) / (8.0 × 10^4 kg)
Speed^2 = (2.2 × 10^9 J) / (8.0 × 10^4 kg)
Speed^2 = 2.75 × 10^4 m^2/s^2
Taking the square root of both sides to solve for speed:
Speed = √(2.75 × 10^4 m^2/s^2)
Speed ≈ 165.7 m/s
Therefore, the speed of the airliner is approximately 165.7 m/s.