I can't comprehend impulse = momentum

[Pushies]

Homework Statement

A satellite with a mass of 1050kg without any momentum or influence of force is floating freely in space. Later, its rocket was activated, applying force of 50N for x seconds. The satellite travelled 1000m in y seconds. Find the time needed, x, to apply 50N.

So i used the equation f = ma to find a so that i can plug it in the equation s = ut + ½at ²

Relevant Equations

F = ma
S = ut + ½at ²

Here is my calculation:

F = ma
50N = 1050kg * a
a = 0.0476m/s²

S = ut + ½at ²
1000m = 0t + ½(0.0476)t²
t = 204.980s
y = 204.980s (time to travel 1000m)

since impulse = momentum,

F * t = mv
F * x = m * distance covered/y
50N * x = 1050kg * 1000m/204.980s
50N * x = 5122.450N⋅s
x = 102.440s

50N * 102.440s ≈ 1050kg * 4.88m/s

Does this mean that the rocket has to apply thrust of 50N for 102.440s to supply the speed needed to cover 1000m in 204.98s ?

 

[etotheipi]

The wording is slightly confusing to me. Is the time interval $y$ measured after the burn has completed? Otherwise it seems to me that there are infinitely many solutions to this question.

(N.B. Also a tiny quibble from me, the impulse $I$ equals the change in momentum $\Delta P$. But in your case, if the initial momentum is 0, the impulse is the final momentum.)

 

[DrClaude]

Here is my calculation:

F = ma
50N = 1050kg * a
a = 0.0476m/s²

S = ut + ½at ²
1000m = 0t + ½(0.0476)t²
t = 204.980s
y = 204.980s (time to travel 1000m)

You are making the assumption that the rocket is activated for all the time it takes to reach 1000 m, which I think is incorrect.

The way I read the problem, you have two unknowns, x and y. What you will then get is x as a function of y. (Even if the rocket is activated for 1 s, it will eventually travel a distance of 1000 m, taking longer than of the rocket is activated for a longer time.)

 

[Pushies]

Sorry for the confusion guys. Iwas tired at the moment of writing, now i can solve it after some time of contemplating. Thanks