To answer this question, you need to know the definition of Relative Motion:
The motion is relative when it depends on a reference point or referencial system. If you know the reference point, you can determine the velocity of an object.
If you are sitting on your chair, you are not moving relative to it (Your speed is 0 km/s); but as you know, our planet moves around the Sun (Traslation Movement) with a speed of 30.0 km/s. Therefore, you are moving 30.0 km/s relative to the sun.
Answer:
If there was no air resistance
Explanation:
We know that free fall is a unique motion in which gravity only works on one object. Objects that are said to be free-falling do not experience a significant force of air resistance; They come under the sole effect of gravity. Under such conditions, all objects fall under the same acceleration, regardless of their mass.
W=20 e(-kt)
A. Rearranging gives k= -(ln(w/20)/t
Substituting w= 10 and solving gives k=0.014
B. Using W=20e(-kt). After 0 hours, W=20. After 24 hours, W=14.29g. After 1 week (24x7=168h) W=1.9g
C. Rearranging gives t=-(ln(10/20)/k. Substituting w=1 and solving gives t=214 hours.
D. Differentiating gives dW/ dt = -20ke(-kt). Solving for t=100 gives dW/dt = 0.07g/h. Solving for t=1000 gives 0.0000002g/h
E. dW/dt = -20ke(-kt). But W=20e(-kt) so dW/dt = -kW
The gravitational force between <em>m₁</em> and <em>m₂</em> has magnitude

while the gravitational force between <em>m₁</em> and <em>m₃</em> has magnitude

where <em>x</em> is measured in m.
The mass <em>m₁</em> is attracted to <em>m₂</em> in one direction, and attracted to <em>m₃</em> in the opposite direction such that <em>m₁</em> in equilibrium. So by Newton's second law, we have

Solve for <em>x</em> :

The solution with the negative square root is negative, so we throw it out. The other is the one we want,

A. 9 J
In a force-distance graph, the work done is equal to the area under the curve in the graph.
In this case, we need to extrapolate the value of the force when the distance is x=30 cm. We can easily do that by noticing that there is a direct proportionality between the force and the distance:

where k is the slope of the line. We can find k, for instance chosing the point at x=5 cm and F=10 N:

And now we can calculate the work by calculating the area under the curve until x=30 cm, F=60 N:

B. 24.5 m/s
The mass of the arrow is m=30 g=0.03 kg. The kinetic energy of the arrow when it is released is equal to the work done by pulling back the bow for 30 cm:

where m is the mass of the arrow and v is its speed. By re-arranging the formula and using W=9 J, we find the speed:
