The orbital velocity of the Earth about the sun is 30 km/s. If the Earth were suddenly stopped in its tracks, it would simply fall radially into the sun. Devise a plan whereby a rocket loaded with radioactive wastes could be fired into the sun for permanent disposal. How fast and in what direction with respect to the Earth's orbit should the rocket be fired?

Planet will crash on to the Sun if the tangential velocity becomes zero and Rocket should be fired  from Earth's orbit is at 30 m/s and in opposite direction to the Earth orbits the Sun

Explanation:

The orbital velocity of the Earth about the sun is 30 km/s. If we shoot a rocket with 30 km/s with respect to Earth in the opposite direction.  Then the two velocity vectors cancel. The resultant velocity would be zero with respect to the Sun. resulting velocity is called as tangential velocity.

Planet will crash on to the Sun if the tangential velocity becomes zero and Rocket should be fired  from Earth's orbit is at 30 m/s and in opposite direction to the Earth orbits the Sun