A rocket of total mass 3100 is traveling in outer space with a velocity of 120 . To alter its course by 40.0, its rockets can be fired briefly in a direction perpendicular to its original motion.
To answer this question, we need to use the principle of conservation of momentum.
The momentum of an object is calculated by multiplying its mass by its velocity. In this case, the rocket's initial momentum can be calculated as:
Initial momentum = Mass * Velocity
Given:
Mass of the rocket = 3100 kg
Velocity of the rocket = 120 m/s
Initial momentum = 3100 kg * 120 m/s = 372,000 kg·m/s
Next, let's consider the change in momentum when the rocket alters its course. The change in momentum is equal to the impulse imparted by the rockets in the perpendicular direction, which can be calculated as:
Change in momentum = Mass * Change in velocity
Given:
Change in velocity = 40 m/s
Change in momentum = 3100 kg * 40 m/s = 124,000 kg·m/s
To alter the rocket's course, the change in momentum must be equal to the negative of its initial momentum. So, we can set up the following equation:
Change in momentum = -Initial momentum
124,000 kg·m/s = -372,000 kg·m/s
Therefore, the rockets must provide a change in momentum of 124,000 kg·m/s in the perpendicular direction to alter the rocket's course by 40 m/s.