What speed would a fly with a mass of 0.61 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 of the fly, we need to compare its kinetic energy to that of the automobile.
The kinetic energy (KE) of an object is given by the formula:
KE = (1/2) * m * v^2
where KE is the kinetic energy, m is the mass of the object, and v is the velocity.
First, let's find the kinetic energy of the automobile. Given that the mass (m₁) of the automobile is 1250 kg and its velocity (v₁) is 11 m/s, we can calculate the kinetic energy using the formula:
KE₁ = (1/2) * m₁ * v₁^2
Plugging in the values, we get:
KE₁ = (1/2) * 1250 kg * (11 m/s)^2
KE₁ = 75625 J
Now, let's find the velocity (v₂) of the fly with a mass (m₂) of 0.61 g (or 0.00061 kg). We can rearrange the formula for kinetic energy and solve for v₂:
KE₂ = (1/2) * m₂ * v₂^2
Since we want to find the velocity of the fly, let's solve for v₂ by rearranging the equation:
v₂^2 = (2 * KE₂) / m₂
v₂ = √((2 * KE₂) / m₂)
Now, substitute KE₂ with the value of KE₁ (kinetic energy of the automobile) to find the velocity of the fly:
v₂ = √((2 * 75625 J) / 0.00061 kg)
v₂ ≈ 1474.04 m/s
Therefore, the fly with a mass of 0.61 g would need to be traveling at approximately 1474.04 m/s to have the same kinetic energy as a 1250 kg automobile traveling at a speed of 11 m/s.