Final answer:
To find the speed of the airliner, we use the kinetic energy formula, rearranged to solve for velocity. After calculating with the given mass and kinetic energy, we determine the airliner's speed to be approximately 552.61 m/s.
Step-by-step explanation:
The student's question involves calculating the speed of an airliner based on its kinetic energy and mass. The formula for kinetic energy (KE) is:
KE = ½ * m * v²
Where KE is the kinetic energy, m is the mass, and v is the velocity (speed). We rearrange the formula to solve for v:
v = √(2 * KE / m)
Given the provided values:
- m = 8.5 x 10⁴ kg (airliner's mass)
- KE = 1.3 x 10⁹ J (airliner's kinetic energy)
We calculate the airliner's speed as follows:
v = √(2 * 1.3 x 10⁹ J / 8.5 x 10⁴ kg)
v = √(2.6 x 10⁹ J / 8.5 x 10⁴ kg)
v = √(305882.35 J/kg)
v ≈ 552.61 m/s
Therefore, the speed of the 8.5 x 10⁴ kg airliner, with a kinetic energy of 1.3 x 10⁹ J, is approximately 552.61 m/s.