Answer
Given:
Wavelength = λ = 18.7 cm
= 0.187 m
Amplitude, A = 2.34 cm
Velocity, v = 0.38 m/s
A) Calculate the angular frequency.
Angular frequency,
ω = 2π f
ω = 2π x 2.03
ω = 12.75 rad/s
B) Calculate the wave number:
C)
Since the wave is traveling in the -x direction, the sign is positive between x and t
y (x, t) = A sin(k x - ω t)
y (x, t) = 2.34 sin(33.59 x - 12.75 t)
Answer:
19.62 ms
Explanation:
t = Time taken = 2 s
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration due to gravity = 9.81 m/s² (we take downward direction as positive)
Using the equations of motion
The pebble's speed upon contact with the water is 19.62 ms
Answer:
0.0984
Explanation:
The first diagram below illustrates a free body diagram that will aid in resolving this problem.
According to the diagram, the force's horizontal component can be expressed as:
Substituting 42° for θ and 87.0° for
Meanwhile, the vertical component is:
Again substituting 42° for θ and 87.0° for
In resolving the vector, let A denote the components in mutually perpendicular directions.
The magnitudes of both components are illustrated in the second diagram provided and can be represented as A cos θ and A sin θ
The frictional force can be expressed as:
Where;
is the coefficient of friction
N = the normal force
Also, the normal reaction (N) is calculated as mg - F sin θ
Substituting . Normal reaction becomes:
By balancing the forces, the horizontal component of the force equals the frictional force.
The horizontal component is described as follows:
Rearranging the equation above to isolate leads to:
Substituting in the following values:
m = 73 kg
g = 9.8 m/s²
Thus:
Therefore, the coefficient of friction is = 0.0984
Response:
E = ρ ( R1²) / 2 ∈o R
Clarification:
Provided information
Two cylinders are aligned parallel
Distance = d
Radial distance = R
d < (R2−R1)
To determine
Express the response using the variables ρE, R1, R2, R3, d, R, and constants
Solution
We have two parallel cylinders
therefore, area equals 2 R × l
And we apply Gauss's Law
EA = Q(enclosed) / ∈o......1
Initially, we calculate Q(enclosed) = ρ Volume
Q(enclosed) = ρ ( R1² × l )
Thus, inserting all values into equation 1
produces
EA = Q(enclosed) / ∈o
E(2 R × l) = ρ (
R1² × l ) / ∈o
This simplifies to
E = ρ ( R1²) / 2 ∈o R
Answer:
Jari
Explanation:
To determine who is traveling faster, we need to evaluate their gradients. A steeper slope indicates a higher speed.
For Jari's path, starting point is (0, 0) and (6, 7) is another point.
The gradient is the difference in y divided by the difference in x:
Change in y=7-0=7
Change in x=6-0=6
Thus, the slope equals 7/6.
For Jade, her first point is (0, 10) and another is (6, 16).
Change in y=16-10=6
Change in x=6-0=6
Thus, the slope equals 6/6=1.
It's evident that 7/6 exceeds 6/6 or 1, proving Jari is quicker than Jade.
