Calculate the speed of an 7.6×104 kg airliner
with a kinetic energy of 1.2 × 109 J.
Answer in units of m/s
To calculate the speed of an airliner with a given kinetic energy, we can use the formula for kinetic energy:
KE = (1/2) * m * v^2,
where KE is the kinetic energy, m is the mass of the airliner, and v is the speed.
In this case, we are given the kinetic energy (KE = 1.2 × 10^9 J) and the mass of the airliner (m = 7.6 × 10^4 kg). We need to rearrange the formula to solve for v.
Rearranging the formula, we have:
2 * KE = m * v^2.
Dividing both sides by m, we get:
2 * KE / m = v^2.
Taking the square root of both sides, we get:
v = √(2 * KE / m).
Now we can substitute the given values into the formula:
v = √(2 * 1.2 × 10^9 J / 7.6 × 10^4 kg).
Evaluating the expression, we get:
v = √(1.57 × 10^4 m^2/s^2).
Finally, taking the square root, we get the speed:
v = 125 m/s (rounded to three significant figures).
Therefore, the speed of the airliner is approximately 125 m/s.
To find the speed of the airliner, we can use the formula for kinetic energy:
Kinetic energy (KE) = 0.5 * mass * velocity^2
Given that the kinetic energy is 1.2 × 10^9 J and the mass of the airliner is 7.6 × 10^4 kg, we can rearrange the formula and solve for velocity:
velocity = √(2 * KE / mass)
Plugging in the given values:
velocity = √(2 * 1.2 × 10^9 J / 7.6 × 10^4 kg)
Simplifying,
velocity = √(1.58 × 10^4 m^2/s^2)
Taking the square root,
velocity ≈ 125.8 m/s
Therefore, the speed of the airliner is approximately 125.8 m/s.
.5 (7.6 * 10^4) v^2 = 1.2 * 10^9
v^2 = .3158 * 10^5
or
v^2 = 3.158 * 10^4
v = 1.78 * 10^2
or
v = 178 m/s