Chapter 7, Problem 16TE

To determine

The speed and direction of the rocket.

Answer to Problem 16TE

The speed of the rocket should be $30\text{km}/\text{s}$ and direction should opposite to the rotation of the Earth to crash the rocket loaded with radioactive waste onto the sun.

Explanation of Solution

The speed for the movement of the object in the orbit of any planet is called the orbital speed of the object. It is the minimum speed for the object to move in the orbit of the planet.

The two-component of the velocity of the revolving object are tangential components and a radial component. The object will fall into the Earth if the tangential component of the object becomes zero.

The rocket crashes into the sun if the tangential velocity of the Earth becomes zero. The rocket should be launched with $30\text{km}/\text{s}$ opposite to the rotation of the Earth to crash it onto the sun.

Conclusion:

Therefore, the speed of the rocket should be $30\text{km}/\text{s}$ and direction should opposite to the rotation of the Earth to crash the rocket loaded with radioactive waste onto the sun.