Answer:
R = 1.8 m
Explanation:
This is a simple harmonic movement exercise, at the bottom of the swing the acceleration is vertical upwards and the speed is tangential to the trajectory, that is horizontal; the expression for the centralized acceleration is
= v² / R
R = v² /a_{c}
where the radius is equal to the length of the swing
let's calculate
R = 8.1 / 4.5
R = 1.8 m
Answer:
x = 7.62 m
Explanation:
First we need to calculate the weight of the rocket:
W = mg
we will use the gravity as 9.8 m/s². We have the mass (500 g or 0.5 kg) so the weight is:
W = 0.5 * 9.8 = 4.9 N
We know that the rocket exerts a force of 8 N. And from that force, we also know that the Weight is exerting a force of 4.9. From here, we can calculate the acceleration of the rocket:
F - W = m*a
a = F - W/m
Solving for a:
a = (8 - 4.9) / 0.5
a = 6.2 m/s²
As the rocket is accelerating in an upward direction, we can calculate the distance it reached, assuming that the innitial speed of the rocket is 0. so, using the following expression we will calculate the time which the rocket took to blast off:
y = vo*t + 1/2 at²
y = 1/2at²
Solving for t:
t = √2y/a
t = √2 * 20 / 6.2
t = √6.45 = 2.54 s
Now that we have the time, we can calculate the horizontal distance:
x = V*t
Solving for x:
x = 3 * 2.54 = 7.62 m
Answer:

Explanation:
Using the given equation, we calculate the energy associated with the excited state
and 

Helium has an atomic number (Z) equal to 2, for n=8:

For n=4:

When an electron jumps from an energy level with greater energy
to one with lower energy
the wavelength of the emitted photon is given by:

h is the Planck constant and c the speed of light in vaccum. So, we have:

The newer ones are at the top and older at the bottom.
Answer:
Part A:
(a): -121.26 ft/s.
(b): -121.13 ft/s.
(c): -121.052 ft/s.
(d): -121.026 ft/s.
Part B:
-121.00 ft/s.
Explanation:
Given that the height of the balloon after t seconds is

The average velocity of an object is defined as the total distance traveled by the object divided by the time taken in covering that distance.

where,
are the positions of the object at time
and
respectively.
<h2><u>
Part A:</u></h2><h2 />
- For the average velocity for the time period beginning when t=3 and lasting .01 sec.
For this case,
- For the average velocity for the time period beginning when t=3 and lasting .005 sec.
For this case,

- For the average velocity for the time period beginning when t=3 and lasting .002 sec.
For this case,

- For the average velocity for the time period beginning when t=3 and lasting .001 sec.
For this case,

<h2><u>
Part B:</u></h2>
The instantaneous velocity of the balloon at the given time is defined as the rate of change of its position at that time.

<u>Note:</u><em> The negative sign with all the velocities indicates that the direction of these velocities are downwards.</em>
<em> </em>