Question

In order to keep a malfunctioning satellite from falling into the earth, space agency officials decide to use a powerful rocket. At the time the rocket is attached, the satellite will be traveling with an initial velocity, Vo, and for every second that the rocket fires, it will add approximately 180 meters per second to this velocity. In order to ensure safety on earth, the velocity must be increased to at least 3,800 m/s. Also, the rocket can fire for no more than 4 seconds.

For the initial velocity of the satellite, Vo, which of the following systems of inequalities best models this situation, where t is time, in seconds, after the rocket is first fired?

A) Vo + 180t ≥ 3800 and t ≤ 4
B) Vo + 180t ≥ 3800 and t < 4
C) Vo + 180t > 3800 and t ≤ 4
D) Vo + 180t > 3800 and t < 4

Answer 1

The correct system of inequalities to model the satellite's required velocity increase with the time constraints of the rocket's firing capability is A) Vo + 180t ≥ 3800 and t ≤ 4.

Step-by-step explanation:

To determine the correct system of inequalities to model the situation described in the question, we consider two constraints: the velocity that the satellite must exceed and the maximum time the rocket can fire. Since the satellite's final velocity must reach or exceed 3,800 m/s for safety, the first inequality will involve ≥ (greater than or equal to). This considers scenarios where reaching exactly 3,800 m/s is acceptable. The second constraint is the maximum firing time of the rocket, which is stated to be no more than 4 seconds. This leads us to a ≤ (less than or equal to) inequality because exactly 4 seconds is permissible. Therefore, the system of inequalities that best models this situation is A) Vo + 180t ≥ 3800 and t ≤ 4.