Solving Astronaut Problem: Force & Acceleration

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Three astronauts are pushing a 127 kg satellite in space using jetpacks, applying three different forces at various angles. The total force needs to be calculated by resolving each force into its horizontal and vertical components. The initial attempt at solving the problem involved incorrect signs for the forces, particularly in the horizontal direction. After clarification, the correct approach was to ensure that opposing forces were accurately represented in the calculations. The discussion concludes with the user successfully finding the correct acceleration after addressing the sign errors in their equations.
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Homework Statement



Three astronauts equipped with jetpacks are pushing a satellite, having a mass of 127 kg, through space. The forces being exerted on the satellite are F1=31.7 N at an angle of 30.8 degrees above the horizontal, F2=40.2 N at 58.6 degrees below the horizontal, and F3=53.9 N along the horizontal.

What is the magnitude of the satellite's acceleration?


Homework Equations



okay so i thought of finding the total force and then using f=ma.

The Attempt at a Solution



31.7N : 31.7sin30.8, 31.7cos30.8
40.2N: -40.2sin58.6, -40.2cos58.6
53.9N: 53.9sin0, 53.9cos0

i added the sin together and cos together and used Pythagorean Theorem to find the total force and plug that into the equation and i got the answer wrong so i don't know where it's wrong. Plz help..
 

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What answer did you get? I've worked it out and will compare yours to mine.

Jared
 
Here's a hint, the vertical velocities are opposing each other so one is + and one is - (Sin values are correct). Your problem is you have also made your equation so that the horizontal force of the lower guy (below horizontal) is opposing the other two.

Jared
 
Last edited:
oh! omg..okay i got it it was suppose to be +40.2cos58.6..
tytytytyty!
 
There we go, glad to help.

Jared
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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