A rocket moves horizontally with a constant velocity u at a height 1. A gu lded missile is fired vertically with a speed v when the rocket passes above it. Assuming that the missile always aims at the rocket with the constant speed v, find the time after which the missile strikes the rocket.

A relativistic rocket emits a gas jet with non-relativistic velocity u constant relative to the rocket. Find how the velocity v of the rocket depends on its rest mass m if the initial rest mass of the rocket equals to m_0 .

The equation of motion of a missile are x = 3t, y = -4t, z = t, where the time ‘t’ is given in seconds, and the distance is measured in kilometres. Based on the above answer the following: At a certain instant of time, if the missile is above the sea level, where the equation of the surface of sea is given by 2x + y + 3z = 1 and the position of the missile at that instant of time is (1, 1, 2), then the image of the position of the rocket in the sea is

A rocket moves in the absence of external forces by ejecting a steady jet with velocity u constant relative to the rocket. Find the velocity v of the rocket at the moment when its mass is equal to m, if at the initial moment it possessed the mass m_0 and its velocity was equal to zero. Make use of the formula given in the foregoing problem.

A rocket is moving with constant acceleration 6. Assume external forces on it to be zero. Exhaust gases escape with velocity u relative to the rocket. Find how its mass changes with time if its initial mass is m_0 .