The addition of vectors involve both magnitude and direction. In this case, we make use of a triangle to visualize the problem. The length of two sides were given while the measure of the angle between the two sides can be derived. We then assign variables for each of the given quantities.
Let:
b = length of one side = 8 m
c = length of one side = 6 m
A = angle between b and c = 90°-25° = 75°
We then use the cosine law to find the length of the unknown side. The cosine law results to the formula: a^2 = b^2 + c^2 -2*b*c*cos(A). Substituting the values, we then have: a = sqrt[(8)^2 + (6)^2 -2(8)(6)cos(75°)]. Finally, we have a = 8.6691 m.
Next, we make use of the sine law to get the angle, B, which is opposite to the side B. The sine law results to the formula: sin(A)/a = sin(B)/b and consequently, sin(75)/8.6691 = sin(B)/8. We then get B = 63.0464°. However, the direction of the resultant vector is given by the angle Θ which is Θ = 90° - 63.0464° = 26.9536°.
In summary, the resultant vector has a magnitude of 8.6691 m and it makes an angle equal to 26.9536° with the x-axis.
Answer:
the oscillations of the electrons must be in the 10⁸ Hz = 100 MHz range
Explanation:
The speed of a wave of radio, television, light, heat, all are manifestations of electromagnetic waves that are oscillations of electric and magnetic fields that support each other, the speed of all these waves is the same and the vacuum is equal to c = 3 108 m / s
All waves have a relationship between the speed of the wave, its frequency and wavelength
c = λ f
f = c /λ
for this case lam = 1 m
f = 3 10⁸/1
f = 3 10⁸ Hz
the oscillations of the electrons must be in the MHz range
It should be clarified that the speed of light in air is a little lower
n = c / v
v = c / n
the refractive index of vacuum is n = 1 and the refractive index of air is n = 1.000002
Answer:
Answer:
28.025 Nm
Explanation:
Angular acceleration, α = 29.5 rad/s^2
oment of inertia, I = 0.95 kg m^2
The torque is defined as
τ = I x α
τ = 0.95 x 29.5
τ = 28.025 Nm
Thus, the torque is 28.025 Nm.
Explanation:
11.86 years. Usually memorized as "12 years".
Answer:
v₂ = 5.7 m/s
Explanation:
We will apply the law of conservation of momentum here:
where,
Total Initial Momentum = 340 kg.m/s
m₁ = mass of bike
v₁ = final speed of bike = 0 m/s
m₂ = mass of Sheila = 60 kg
v₂ = final speed of Sheila = ?
Therefore,
<u>v₂ = 5.7 m/s </u>
