Answer:
a) V = 0.82m/s
b) Vmax = 0.985 m/s
Explanation:
By conservation of energy we know that:
Eo = Ef 
Solving for V we get:
V = 0.82 m/s
To find the maximum speed we will do the same to an intermediate point where the compression is X and the distance for the work donde by frictions is given by (Xmax - X) = (0.28m - X):

Then we have to solve for V, derive and equal zero in order to find position X. After solving the derivative we get:
X = 0.1m Replacing this value into the equation for Vmax:
Vmax = 0.985m/s
Answer: 0.55 m/s
Explanation:
This situation is related to projectile motion (also called parabolic motion), where the main equations are as follows:
(1)
(2)
Where:
is the horizontal displacement of the pencil
is the pencil's initial velocity
since we are told the pencil rolls <u>horizontally</u> before falling
is the time since the pencil falls until it hits the ground
is the initial height of the pencil
is the final height of the pencil (when it finally hits the ground)
is the acceleration due gravity, always acting vertically downwards
Begining with (1):
(3)
(4)
Finding
from (2):
(5)
(6)
Substituting (6) in (4):
(7)
Isolating
:
(8)
(9)
Finally:
Explanation:
Since, it is given that one hand completes 3.19 vibrations in 8.46 sec. Therefore, in one second the number of vibrations will be as follows.

= 0.377 vibrations
Hence, frequency (f) = 0.38 Hz
Now, formula to calculate the speed is as follows.
v = 
or,
= 
= 1.57 cm
Thus, we can conclude that the wavelength is 1.57 cm.
A hydrogen<span> atom contains 1 </span>electron<span>, 1 proton, and no neutrons based on the Periodic Table. The isotopes of the </span>hydrogen<span> atoms however, do contain neutrons.</span>