Answer:
<em>The speed of the passengers is 5.24 m/s</em>
Explanation:
<u>Uniform Circular Motion
</u>
It occurs when an object in a circular path travels equal angles in equal times.
The angular speed can be calculated in two different ways:
Where:
v = tangential speed
r = radius of the circle described by the rotating object
Also:
Where:
f = frequency
Since the frequency is calculated when the number of revolutions n and the time t are known:
The Ferris wheel has a diameter of 100 m and makes n=1 rotation in t=60 seconds, thus the frequency is:
The angular speed is:
Now we calculate the tangential speed, solving this formula for v:
The radius is half the diameter, r=100/2=50 m:
Calculating:
v = 5.24 m/s
The speed of the passengers is 5.24 m/s
Answer:
Approximately 
, assuming that the rocket had no propulsion onboard, and that air resistance on the rocket is negligible.
Explanation:
Initial velocity of this rocket: 
.
When the rocket is at its maximum height, the velocity of the rocket would be equal to 
. That is: 
.
The acceleration of the rocket (because of gravity) is constantly downwards, with a value of 
.
Let 
denote the distance that the rocket travelled from the launch site to the place where it attained maximum height. The following equation would relate 
to 
, 
, and 
:
.
Apply this equation to find the value of :
.
In other words, the maximum height that this rocket attained would be 
.
Again, assume that the air resistance on this rocket is negligible. The rocket would return to the ground along the same path, and would cover a total distance of 
.
First, let us derive our working equation. We all know that pressure is the force exerted on an area of space. In equation, that would be: P = F/A. From Newton's Law of Second Motion, force is equal to the product of mass and gravity: F = mg. So, we can substitute F to the first equation so that it becomes, P = mg/A. Now, pressure can also be determined as the force exerted by a fluid on an area. This fluid can be measure in terms of volume. Relating volume and mass, we use the parameter of density: ρ = m/V. Simplifying further in terms of height, Volume is the product of the cross-sectional area and the height. So, V = A*h. The working equation will then be derived to be:
P = ρgh
This type of pressure is called the hydrostatic pressure, the pressure exerted by the fluid over a known height. Next, we find the literature data of the density of seawater. From studies, seawater has a density ranging from 1,020 to 1,030 kg/m³. Let's just use 1,020 kg/m³. Substituting the values and making sure that the units are consistent:
P = (1,020 kg/m³)(9.81 m/s²)(11 km)*(1,000 m/1km)
P = 110,068,200 Pa or 110.07 MPa
