Answer:
All three pendulums will have the same angular frequencies.
Explanation:
For a simple pendulum, the time period using the approximation 
is expressed as:
The angular frequency 
is defined as
Since the angular frequency remains unaffected by the initial angle (valid strictly for small angle approximations), we deduce that the angular frequencies of the three pendulums are identical.
Definamos h como la distancia que hay desde el borde del pozo hasta la superficie del agua (en metros).
Consideremos la gravedad g como 9.8 m/s² y despreciemos la resistencia del aire.
La velocidad inicial vertical del guijarro es nula.
Ya que el guijarro impacta el agua tras 1.5 segundos, entonces:
h = 0.5 * (9.8 m/s²) * (1.5 s)² = 11.025 m
Resultado: 11.025 m
Flow rate calculations yield 220 cans, each with a volume of 0.355 l, leading to 78.1 l/min or 1.3 l/s or 0.0013 m³/s.
At Point 2:
A2 = 8 cm² = 0.0008 m²
V2 = Flow rate/A2 = 0.0013/0.0008 = 1.625 m/s
P1 = 152 kPa = 152000 Pa
At Point 1:
A1 = 2 cm² = 0.0002 m²
V1 = Flow rate/A1 = 0.0013/0.0002 = 6.5 m/s
P1 =?
Height = 1.35 m
Using Bernoulli’s principle;
P2 + 1/2 * V2² / density = P1 + 1/2 * V1² / density + density * gravitational acceleration * height
=> 152000 + 0.5 * (1.625)² * 1000 = P1 + 0.5 * (6.5)² * 1000 + (1000 * 9.81 * 1.35)
=> 153320.31 = P1 + 34368.5
=> P1 = 1533210.31 - 34368.5 = 118951.81 Pa = 118.95 kPa
The second question necessitates a figure to provide an answer. For the initial question
The acceleration of the sack is
1.5² - 0² = 2a(0.2)
a = 5.63 m/s²
The ramp's reaction force is
F = 8 kg (5.63 m/s²)
F = 45 N
Differentiate the kinematic equation with respect to time to find the velocity's rate of increase.
assuming north-south is along the Y-axis and east-west along the X-axis
X = total X-displacement
from the graph, total displacement in the X-direction is computed as
X = 0 - 20 + 60 Cos45 + 0
X = 42.42 - 20
X = 22.42 m
Y = total Y-displacement
from the graph, total displacement in the Y-direction is computed as
Y = 40 + 0 + 60 Sin45 + 50
Y = 90 + 42.42
Y = 132.42 m
To calculate the magnitude of the net displacement vector, we apply the Pythagorean theorem, yielding
magnitude: Sqrt(X² + Y²) = Sqrt(22.42² + 132.42²) = 134.31 m
Direction: tan⁻¹(Y/X) = tan⁻¹(132.42/22.42) = 80.4 deg north of east
