Acceleration due to gravity will be constant, but the speed can change.
The distance for any rectilinear motion at constant acceleration is:
d = v₀t + 0.5at²
where
v₀ is the initial velocity
So, if v₀ = 6v, and it stopped to 0 m/s, then the acceleration is equal to:
a = (0 - 6v)/t = -6v/t
Thus,
d = (6v)(t) + (0.5)(-6v/t)(t²)
d = 6vt - 3t
<span>d = 3t(2v - 1)</span>
To solve this problem we will apply the concepts related to centripetal acceleration, which will be the same - by balance - to the force of gravity on the body. To find this acceleration we must first find the orbital velocity through the Doppler formulas for the given periodic signals. In this way:

Here,
Orbital Velocity
Maximal Wavelength
Average Wavelength
c = Speed of light
Replacing with our values we have that,

<em>Note that the average signal is 3.000000m</em>

Now using the definition about centripetal acceleration we have,

Here,
v = Orbit Velocity
r = Radius of Orbit
Replacing with our values,



Applying Newton's equation for acceleration due to gravity,

Here,
G = Universal gravitational constant
M = Mass of the planet
r = Orbit
The acceleration due to gravity is the same as the previous centripetal acceleration by equilibrium, then rearranging to find the mass we have,



Therefore the mass of the planet is 
Answer:
a) -31.36 m/s
b) 50.176 m
Explanation:
<h2>a) Velocity of the bag</h2>
This is a problem of motion in one direction (specifically vertical motion), and the equation that best fulfills this approach is:
(1)
Where:
is the final velocity of the supply bag
is the initial velocity of the supply bag (we know it is zero because we are told <u>it was "dropped", this means it goes to ground in free fall</u>)
is the acceleration due gravity (the negtive sign indicates the gravity is downwards, in the direction of the center of the Earth)
is the time
Knowing this, let's solve (1):
(2)
Hence:
Note the negative sign is because the direction of the bag is downwards as well.
<h2>b) Final height of the bag</h2>
In this case we will use the following equation:
(3)
Where:
is the distance the bag has fallen
remembering <u>the bag was dropped</u>
is the acceleration due gravity (downwards)
is the time
Then:
(3)
(4)
Finally:
Answer: 10.5 kJ
Explanation:
In order to be able to solve this problem, you will need to know the value of water's specific heat, which is listed as
c
=
4.18
J
g
∘
C