200kg Astronaut, 2.0 m/s, 100.0 N rocket ?

[jacksonjw81]

[SOLVED] 200kg Astronaut, 2.0 m/s, 100.0 N rocket ?

A 200.0 kg astronaut and equipment move with a velocity of 2.00 m/s toward an orbiting spacecraft . How long will the astronaut need to fire a 100.0 N rocket backpack to stop the motion relative to the spacecraft ? Give your answer in s.

Homework Equations

F=ma
W=mg
m=w/g
a=F/m

The Attempt at a Solution

I know I am missing something so simple. I have spent too long trying to solve this problem and have given up.

F=(200kg)(2 m/s)=400 kg*m/s=
F=400N/s

I don't know what to do with the 100N for the rocket pack, I'm getting lost in all the different conversions.

Please Help

 

[iloveflickr]

Why don't you start by applying 100N for one second, and see what the final speed is?

There is definitely a way to apply the equations, but understand it intuitively and it'll make more sense.

Also, in your "F=(200kg)(2 m/s)=400 kg*m/s^2", you have an extra 1/s on the right side.

 

[D H]

F=(200kg)(2 m/s)=400 kg*m/s^2

Look again at the units. That should be 200\,\text{kg} 2\,\text{m}/\text{s} = 400 \,\text{kg-m}/\text{s}. The product of velocity and mass is momentum, not force. An alternative expression for kg-m/s is Newton-seconds. That 400 kg-m/sec is the same as 400 Newton-seconds, and this form should tell you exactly how long the rocket pack needs to be fired.

 

[jacksonjw81]

Look again at the units. That should be 200\,\text{kg} 2\,\text{m}/\text{s} = 400 \,\text{kg-m}/\text{s}. The product of velocity and mass is momentum, not force. An alternative expression for kg-m/s is Newton-seconds. That 400 kg-m/sec is the same as 400 Newton-seconds, and this form should tell you exactly how long the rocket pack needs to be fired.

So if the Astronaut has a Force of 400 Newton-seconds and he fires a 100 N rocket then the answer will be 4 s?

If that is the correct answer I'm going to be pissed that is the solution I came up with when I first began working this problem. But, thought that it was to easy and couldn't be right.

 

[iloveflickr]

Pretty much. For each 100N force applied for 1 second, the decrease in velocity is 0.5m/s.

In 4 seconds, -2.0 m/s decrease in velocity.

Enjoy.

 

[jacksonjw81]

Pretty much. For each 100N force applied for 1 second, the decrease in velocity is 0.5m/s.

In 4 seconds, -2.0 m/s decrease in acceleration.

Enjoy.

Thanks