A) 0
because all of the forces cancel out, so it is not moving with balanced forces.
Answer:
(a) r = 1.062·R
= ![\frac{531}{500} R_E](https://tex.z-dn.net/?f=%5Cfrac%7B531%7D%7B500%7D%20R_E)
(b) r = ![\frac{33}{25} R_E](https://tex.z-dn.net/?f=%5Cfrac%7B33%7D%7B25%7D%20R_E)
(c) Zero
Explanation:
Here we have escape velocity v
given by
and the maximum height given by
![\frac{1}{2} v^2-\frac{GM}{R_E} = -\frac{GM}{r}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20v%5E2-%5Cfrac%7BGM%7D%7BR_E%7D%20%3D%20-%5Cfrac%7BGM%7D%7Br%7D)
Therefore, when the initial speed is 0.241v
we have
v =
so that;
v² =
v² = ![{\frac{0.116162\times GM}{R_E} }](https://tex.z-dn.net/?f=%7B%5Cfrac%7B0.116162%5Ctimes%20GM%7D%7BR_E%7D%20%7D)
is then
![\frac{1}{2} {\frac{0.116162\times GM}{R_E} }-\frac{GM}{R_E} = -\frac{GM}{r}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%7B%5Cfrac%7B0.116162%5Ctimes%20GM%7D%7BR_E%7D%20%7D-%5Cfrac%7BGM%7D%7BR_E%7D%20%3D%20-%5Cfrac%7BGM%7D%7Br%7D)
Which gives
or
r = 1.062·R
(b) Here we have
![K_i = 0.241\times \frac{1}{2} \times m \times v_e^2 = 0.241\times \frac{1}{2} \times m \times \frac{2GM}{R_E} = \frac{0.241mGM}{R_E}](https://tex.z-dn.net/?f=K_i%20%3D%200.241%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20m%20%5Ctimes%20v_e%5E2%20%3D%200.241%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%20m%20%20%5Ctimes%20%5Cfrac%7B2GM%7D%7BR_E%7D%20%3D%20%5Cfrac%7B0.241mGM%7D%7BR_E%7D)
Therefore we put
in the maximum height equation to get
![\frac{0.241}{R_E} -\frac{1}{R_E} =-\frac{1}{r}](https://tex.z-dn.net/?f=%5Cfrac%7B0.241%7D%7BR_E%7D%20-%5Cfrac%7B1%7D%7BR_E%7D%20%3D-%5Cfrac%7B1%7D%7Br%7D)
From which we get
r = 1.32·R
(c) The we have the least initial mechanical energy, ME given by
ME = KE - PE
Where the KE = PE required to leave the earth we have
ME = KE - KE = 0
The least initial mechanical energy to leave the earth is zero.
Answer:
Explanation:
The equation for this is
where f is the frequency, v is the velocity, and lambda is the wavelength. Filling in:
and
which means that
the wavelength is 1.37 m, rounded to the correct number of significant digits.