**Sample Problem**

A rocket whose initial mass Mi is 850 kg consumes fuel at the rate R = 2.3 kg/so The speed of the exhaust gases relative to the rocket engine is 2800 mls.

(a) What thrust does the rocket engine provide

b) What is the initial acceleration of the rocket?

SOLUTION: e can relate the thrust T of a rocket to the magnitude of the resulting acceleration with T = Ma, where M is the rocket’s . The Key Idea, however, is that M decreases and a increases fuel is consumed. Because we want the initial value of a here, e must use the initial value Mi of the mass, finding that

Launched from Earth’s surface, a rocket must have an initial acceleration greater than g = 9.8 m/s2. Put another way, the thrust of the rocket engine must exceed the initial gravitational force.

(c) Suppose, instead, that the rocket is launched from a spacecraft already in deep space, where we can neglect any gravitational force acting on it. The mass MI of the rocket when its fuel is exhausted is 180 kg. What is its speed relative to the spacecraft at that time? Assume that the spacecraft is so massive that the launch does alter its speed.

SOLUTION: Key Idea here is that the rocket’s final speed If (when the fuel is exhausted) depends on the ratio of its initial mass to its final mass. With the initial speed Vi = 0, we have

Note that the ultimate speed of the rocket can exceed the exhaust speed.

### Related Physics Topics for Tuition