Question

A $3000kg$meteorite falls toward the earth. What is the magnitude of the earth’s acceleration just before impact? The earth’s mass is$5.98\times {10}^{24}kg$.

Short answer

The magnitude of the earth’s acceleration just before impact is $4.9163\times {10}^{-21}\mathrm{m}/{\mathrm{s}}^2.$

Step-by-step solution

Given information

The meteorite has a mass of $3000kg$and its acceleration is $9.8m/s^2.$The earth has a mass of $5.98\times {10}^{24}kg.$

Calculation

Here, the earth has a mass of $5.98\times {10}^{24}kg$and the acceleration of the earth is unknown.

The force of gravity exerted on the meteorite by the earth is the same as the force of gravity exerted on the earth by the meteorite, according to Newton's third law.

So, the force of gravity exerted on the meteorite by the earth is given by:-

localid="1649254099207" $$\begin{gathered} F=ma \\ F=3000kg\times 9.8m/s^2 \\ F=29400\mathrm{N} \end{gathered}$$

The same amount of force is exerted on Earth . Its acceleration is given by:-

$$\begin{gathered} F=ma \\ a=F/m \\ a=29400N/5.98\times {10}^{24}kg \\ a=4.9163\times {10}^{-21}\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$

Final answer

The magnitude of the earth’s acceleration just before impact is$4.9163\times {10}^{-21}\mathrm{m}/{\mathrm{s}}^2.$