Use 5.98 × 10

24
kg as the mass of the Earth.
A 2350 kg meteorite has a speed of 143 m/s
just before colliding head-on with the Earth.
Determine the recoil speed of the Earth.
Answer in units of m/s

To determine the recoil speed of the Earth after colliding with the meteorite, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.

The momentum of an object is given by the product of its mass and velocity. So, we can calculate the initial momentum of the meteorite and the Earth, and then equate it to the final momentum after the collision.

To start, let's calculate the initial momentum of the meteorite. We are given the mass (m) and speed (v) of the meteorite, so we can use the equation P = m * v, where P represents momentum.

Initial momentum of the meteorite = 2350 kg * 143 m/s

Next, we need to calculate the initial momentum of the Earth. The given mass of the Earth is 5.98 × 10^24 kg, and since it is at rest initially, its initial velocity is zero.

Initial momentum of the Earth = mass of the Earth * initial velocity of the Earth = 5.98 × 10^24 kg * 0 m/s = 0 kg m/s

Now, let's consider the final momentum after the collision. Since the meteorite collides head-on with the Earth, their velocities will be in opposite directions. After the collision, the meteorite will embed itself into the Earth, resulting in their combined mass moving with a recoil velocity.

Let's assume the recoil velocity of the Earth is v_recoil. As the meteorite becomes a part of the Earth, the final mass of the combined system is the sum of the mass of the Earth and the meteorite (5.98 × 10^24 kg + 2350 kg).

Final momentum = (mass of the Earth + mass of the meteorite) * v_recoil

Now, we equate the initial momentum of the meteorite and the Earth to the final momentum:

Initial momentum of the meteorite + Initial momentum of the Earth = Final momentum

2350 kg * 143 m/s + 0 kg m/s = (5.98 × 10^24 kg + 2350 kg) * v_recoil

Simplifying the equation:

335,050 kg m/s = (5.98 × 10^24 kg + 2350 kg) * v_recoil

Now, we can solve for the recoil velocity (v_recoil):

v_recoil = 335,050 kg m/s / (5.98 × 10^24 kg + 2350 kg)

Calculating the sum of the masses in the denominator:

5.98 × 10^24 kg + 2350 kg = 5.98 × 10^24 kg

Substituting this value back into the equation:

v_recoil = 335,050 kg m/s / (5.98 × 10^24 kg)

Now, we can evaluate this expression using a calculator to get our final answer.

v_recoil ≈ 5.609 × 10^(-22) m/s

Therefore, the recoil speed of the Earth, after colliding with the meteorite, is approximately 5.609 × 10^(-22) m/s.