Physics 40s conservation of momentum question

[Brodo17]

A 10,000kg space shuttle moving east at 3000km/h wishes to change its course by 10°. It does so by ejecting an object at a speed of 5000km/h (South). Calculate the mass of the ejected object.



Equations
Momentum before = momentum after
momentum is mass x velocity


I am honesty pretty well completely stumped on how to solve this question. Would you draw a vector diagram? Usually you figure out the momentum before and then the momentum after must be equal. However I don't know how to do that because when the shuttle releaes the amount of weight, we no longer know its amount of weight or velocity.
Im so confused, please help

 

[Astronuc]

Think of a velocity tranverse to the shuttle's initial velocity, such that is some time t, the resultant velocity is at 10°.

Now to move in that direction, the shuttle must eject an object of mass M at 5000km/h velocity to the south. The shuttle's mass is 10,000kg.

 

[nlightner]

!

I would approach this question by first identifying the given information and what is being asked. We are given the mass and velocity of the space shuttle and the change in its direction. We are also given the velocity of the ejected object. The question is asking for the mass of the ejected object.

Next, I would use the conservation of momentum principle, which states that the total momentum of a system remains constant unless acted upon by an external force. In this case, the system is the space shuttle and the ejected object.

To solve for the mass of the ejected object, we can use the equation: momentum before = momentum after. The momentum before the object is ejected is the momentum of the space shuttle, which can be calculated as:

p1 = m1v1

Where p1 is the momentum, m1 is the mass of the space shuttle, and v1 is its velocity.

The momentum after the object is ejected can be calculated as:

p2 = m2v2

Where p2 is the momentum, m2 is the mass of the ejected object, and v2 is its velocity.

Since momentum is conserved, we can set the two equations equal to each other:

m1v1 = m2v2

We know the values for m1 and v1, so we can rearrange the equation to solve for m2:

m2 = (m1v1)/v2

Plugging in the values, we get:

m2 = (10,000kg * 3000km/h)/5000km/h

m2 = 6000kg

Therefore, the mass of the ejected object is 6000kg.

In conclusion, by applying the conservation of momentum principle and using the given information, we can solve for the mass of the ejected object.