What speed would a fly with a mass of 0.71 g need in order to have the same kinetic energy as a 1250 kg automobile traveling at a speed of 11 m/s?

To find the speed at which a fly with a mass of 0.71 g would need to have the same kinetic energy as a 1250 kg automobile traveling at a speed of 11 m/s, we can use the formula for kinetic energy:

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

Let's first convert the mass of the fly from grams to kilograms:

0.71 g = 0.71 * 10^-3 kg

Now we can calculate the kinetic energy of the automobile using the given mass and velocity:

Kinetic Energy of automobile = 1/2 * 1250 kg * (11 m/s)^2

Next, we can set the kinetic energy of the fly equal to the kinetic energy of the automobile and solve for its velocity:

1/2 * (0.71 * 10^-3 kg) * velocity_fly^2 = 1/2 * 1250 kg * (11 m/s)^2

Simplifying the equation:

0.355 * 10^-3 kg * velocity_fly^2 = 76250 kg * m^2/s^2

Dividing both sides by 0.355 * 10^-3 kg:

velocity_fly^2 = (76250 kg * m^2/s^2) / (0.355 * 10^-3 kg)

velocity_fly^2 ≈ 215493,039 m^2/s^2

Taking the square root of both sides:

velocity_fly ≈ √(215493,039 m^2/s^2)

velocity_fly ≈ 464.54 m/s (rounded to two decimal places)

Therefore, in order to have the same kinetic energy as the automobile, the fly would need to be traveling at approximately 464.54 m/s.

To find the speed of the fly, we need to equate its kinetic energy to that of the automobile.

The formula for kinetic energy is given by:
K.E. = (1/2) * m * v^2

Where K.E. represents kinetic energy, m represents mass, and v represents velocity.

Let's calculate the kinetic energy of the automobile:
K.E. of automobile = (1/2) * m_automobile * v_automobile^2
= (1/2) * 1250 kg * (11 m/s)^2

Now, let's calculate the kinetic energy of the fly using the given mass (0.71 g = 0.00071 kg):
K.E. of fly = (1/2) * m_fly * v_fly^2
= (1/2) * 0.00071 kg * v_fly^2

Since we want the kinetic energy of the fly to be equal to that of the automobile, we have:
(1/2) * 1250 kg * (11 m/s)^2 = (1/2) * 0.00071 kg * v_fly^2

Now we can solve for the velocity of the fly, v_fly:
v_fly = sqrt((1250 kg * (11 m/s)^2) / (0.00071 kg))

Calculating this using a calculator, we find:
v_fly ≈ 560,561 m/s

Therefore, the fly would need a speed of approximately 560,561 m/s to have the same kinetic energy as the 1250 kg automobile traveling at a speed of 11 m/s.

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