A man of mass 50 kg starts moving on the earth and acquires a speed of 1.8 m/s. With what speed does the earth recoil? Mass of the earth = 6 * 10(24) kg.

To find the recoil speed of the Earth when a man starts moving, we can use the principle of conservation of momentum. This principle states that in a closed system, the total momentum before an event must equal the total momentum after that event. In this case, the system consists of the man and the Earth.

Understanding the Scenario

Initially, both the man and the Earth are at rest, so their combined momentum is zero. When the man starts moving, he gains momentum in one direction, and the Earth will gain an equal amount of momentum in the opposite direction to conserve the total momentum of the system.

Calculating the Momentum

The momentum (p) of an object is calculated using the formula:

p = mass × velocity

For the man:

• Mass of the man (m₁) = 50 kg
• Velocity of the man (v₁) = 1.8 m/s
• Momentum of the man (p₁) = m₁ × v₁ = 50 kg × 1.8 m/s = 90 kg·m/s

Now, let’s denote the recoil speed of the Earth as v₂. The mass of the Earth (m₂) is approximately 6 × 10²⁴ kg. The momentum of the Earth (p₂) can be expressed as:

p₂ = m₂ × v₂

Applying Conservation of Momentum

According to the conservation of momentum:

p₁ + p₂ = 0

Substituting the values we have:

90 kg·m/s + (6 × 10²⁴ kg) × v₂ = 0

Solving for v₂

Rearranging the equation gives us:

(6 × 10²⁴ kg) × v₂ = -90 kg·m/s

Now, we can solve for v₂:

v₂ = -90 kg·m/s / (6 × 10²⁴ kg)

v₂ = -1.5 × 10^-23 m/s

Interpreting the Result

The negative sign indicates that the Earth moves in the opposite direction to the man's movement. However, the recoil speed of the Earth is extremely small, about 1.5 × 10^-23 m/s, which is practically imperceptible. This illustrates how massive the Earth is compared to a human, making its recoil speed negligible.

In summary, when the man starts moving at 1.8 m/s, the Earth recoils at a speed of approximately 1.5 × 10^-23 m/s, demonstrating the principle of conservation of momentum in a practical scenario.