Answer:
18.2145 meters
Explanation:
Using the conservation of momentum, we have that:

m1 = m1' is the mass of the astronaut, m2=m2' is the mass of the satellite, v1 and v2 are the inicial speed of the astronaut and the satellite (v1 = v2 = 0), and v1' and v2' are the final speed of the astronaut and the satellite. Then we have that:


The negative sign of this speed just indicates the direction the astronaut goes, which is the opposite direction of the satellite.
If the astronaut takes 7.5 seconds to come into contact with the shuttle, their initial distance is:

Answer:
2 m/s
Explanation:
The first part of the question the car is going in reverse or negative along the x axis. Then the second part the car is moving forward along the x axis. So the car would only have velocity in the current direction of movement. So our equation for velocity is as follows.
v = d/t
v = 10 m/5 s
v = 2 m/s
Answer:
9 cm
-36 cm
Explanation:
u = Object distance
v = Image distance
f = Focal length = 12
m = Magnification = 4

Lens equation

Object distance is 9 cm

Image distance is -36 cm (other side of object)
A) The resultant force is 30.4 N at 
B) The resultant force is 18.7 N at 
Explanation:
A)
In order to find the resultant of the two forces, we must resolve each force along the x- and y- direction, and then add the components along each direction to find the components of the resultant.
The two forces are:
at
above x-axis
at
above y-axis
Resolving each force:


So, the components of the resultant are:

And the magnitude of the resultant is:

And the direction is:

B)
In this case, the 15 N is applied in the opposite direction to the 20 N force. Therefore we need to re-calculate its components, keeping in mind that the angle of the 15 N force this time is

So we have:

So, the components of the resultant this time are:

And the magnitude is:

And the direction is:

Learn more about vector addition:
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