Answer
The answer and procedures of the exercise are attached in the following archives.
Step-by-step explanation:
You will find the procedures, formulas or necessary explanations in the archive attached below. If you have any question ask and I will aclare your doubts kindly.
Answer:
The second dart leaves the gun two times as faster than the first one.
Explanation:
Assuming no energy loss during the spring-dart energy transfer, we have by the conservation of energy principle

Given an arbitrary
and its double,
, launch velocities are

Given that,
Mass of the stone, m = 400 g = 0.4 kg
Initial speed, u = 20 m/s
It is climbed to a height of 12 m.
To find,
The work done by the resistance force.
Solution,
Let v is the final speed. It can be calculated by using the conservation of energy.

Work done is equal to the change in kinetic energy. It can be given as follows :

So, the required work done is 32.99 J.
C. inertia. the man is sent flying off the bus because of his weight and the sudden stop of the bus. this effect is called inertia. an example of gravity would be throwing an apple up and having it come to the ground. an example of weight would be putting a man and an elephant on a scale and having the elephant come down while the man goes up.
To solve this problem it is necessary to apply the concepts related to acceleration due to gravity, as well as Newton's second law that describes the weight based on its mass and the acceleration of the celestial body on which it depends.
In other words the acceleration can be described as

Where
G = Gravitational Universal Constant
M = Mass of Earth
r = Radius of Earth
This equation can be differentiated with respect to the radius of change, that is


At the same time since Newton's second law we know that:

Where,
m = mass
a =Acceleration
From the previous value given for acceleration we have to

Finally to find the change in weight it is necessary to differentiate the Force with respect to the acceleration, then:




But we know that the total weight (F_W) is equivalent to 600N, and that the change during each mile in kilometers is 1.6km or 1600m therefore:


Therefore there is a weight loss of 0.3N every kilometer.