What is the Launch Speed of the Package?

[D. Tran]

Homework Statement

A spaceship is coasting with a constant velocity of 124 m/s. The ship fires a deep space "care package" of mass 1300 kg. The firing of the care package brings the rocket ship to a halt. If the mass of the spaceship, not including the rocket, is 4.0 x 10⁶ kg, what is the launch speed of the package?

Homework Equations

p=mv
ΣP_i=ΣP_f

P_iS=m_sv_s
P_iP=m_pv_p
P_fS=m_sv_s
P_fP=m_sv_s​

ΣP_i=P_iS+P_iP
ΣP_f=P_fS+P_fP

final equation: m_Sv_iS+m_Pv_iP=m_Sv_fS+m_Pv_fP

where s=spaceship and p=package

The Attempt at a Solution

m_S=4.0 x 10⁶ kg
v_iS=124 m/s
v_fS=0
m_P=1300 kg
v_iP=?
v_fP=?

I do not know if the final equation used is correctly applied. After plugging in all of the known variables, there are two unknown. Could someone point me in the general direction?

Thank you for your time and help.

-D. Tran

 

[pgardn]

Homework Statement

A spaceship is coasting with a constant velocity of 124 m/s. The ship fires a deep space "care package" of mass 1300 kg. The firing of the care package brings the rocket ship to a halt. If the mass of the spaceship, not including the rocket, is 4.0 x 10⁶ kg, what is the launch speed of the package?

Homework Equations

p=mv
ΣP_i=ΣP_f

P_iS=m_sv_s
P_iP=m_pv_p
P_fS=m_sv_s
P_fP=m_sv_s​

ΣP_i=P_iS+P_iP
ΣP_f=P_fS+P_fP

final equation: m_Sv_iS+m_Pv_iP=m_Sv_fS+m_Pv_fP

where s=spaceship and p=package

The Attempt at a Solution

m_S=4.0 x 10⁶ kg
v_iS=124 m/s
v_fS=0
m_P=1300 kg
v_iP=?
v_fP=?

I do not know if the final equation used is correctly applied. After plugging in all of the known variables, there are two unknown. Could someone point me in the general direction?

Thank you for your time and help.

-D. Tran

The initial momentum could be written as (mass of package + mass of spaceship)v. The package and spaceship are moving as one to begin with, yes?

All of the above are known.

the final momentum (after the firing or impulse) can be written as you have it and all of the variables are known except the velocity of the package. Which you should now be able to find.

 

[D. Tran]

The initial momentum could be written as (mass of package + mass of spaceship)v. The package and spaceship are moving as one to begin with, yes?

All of the above are known.

the final momentum (after the firing or impulse) can be written as you have it and all of the variables are known except the velocity of the package. Which you should now be able to find.

Is finding the initial velocity of the package the same as finding the launch speed?

 

[PhanthomJay]

As pgardn has noted, the initial velocity of the spaceship, and the initial velocity of the package, are, with respect to a third party observer, the same. The launch speed is the final velocity of the package v_f (its velocity after it has been fired).