A 1000 kg rocket is moving at a constant velocity in deep space. It is moving at 40 meters/second when its burners apply 200 N of force for 300 seconds. What is the final speed after 300 seconds?

Forgive me. When I hear a person say "I'm not quite sure", what I hear is "I have no clue".
This is not an awfully tough problem, but there IS one big piece of information missing: When the 'burners' ignite, do they push in the same direction it's already moving, and speed it up ? Or do they push opposite to its motion, and slow it down ? the question doesn't say.
For reasons that I won't go into, I think we should assume that the 'burners' are on the back of the rocket, pushing in the same direction it's already going, and speeding it up.
So we have a 1,000 kg object. Suddenly a force of 200N kicks it from behind, and starts speeding it up.
Do you remember . . . (Force) = (mass) x (acceleration) ? We know the force and the mass . . . (200N) = (1,000 kg) x (acceleration) Acceleration = 200/1,000 = (0.2 meter per second) per second. That's how its speed grows during the burn. In 300 seconds, it will gain (300) times (0.2 meter per second) = 60 m/sec.
It was originally moving at 40 m/s and the 'burners' added 60 m/s during the 5-minute burn. So when the burners shut off, it's moving 100 m/s .
If the burners were pushing the other way, slowing it down, then in 300 sec it would lose 60 m/s of speed. Its final speed would be (40) + (-60) = -20 m/s. That means 20 m/s in the opposite direction.
That's the answer you need, and the math you use to find it.
But there's still something wrong with this problem ... in the real world of space travel, it's a bogus question. The ship doesn't remain 1,000 kg while the thrusters fire for 5 minutes. The thrusters use fuel to burn, and the mass of the ship keeps decreasing and decreasing while fuel burns.
So when the real aerospace engineers do this same problem, they still use (force) = (mass) x (acceleration), but they're working with a mass that's constantly changing. You can see that this makes the problem a little more complicated, and to work it, they use "Calculus". You can get into Calculus before you graduate High School, if you want to. The things you can do with it can really give you a feeling of power.

Answered by AL2006 | 2024-06-10

After applying a force of 200 N for 300 seconds, the final speed of the 1000 kg rocket increases from 40 m/s to 100 m/s, resulting in a total speed of 100 m/s. This is calculated using Newton's second law to find acceleration, followed by computing the change in velocity over time. The calculation steps include determining acceleration, change in velocity, and final speed based on the initial velocity.
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Answered by AL2006 | 2024-12-24