let the vector Q is given as

given that

here we know that

now by above equation


so by comparing both sides
b = 0
4c - 3a = 6
also we know that


by solving above equation
a = 12.85 and c = 11.14
so the vector Q is given as

Answer:
Explanation:
kinetic energy = 14.1 MJ = 14.1 x 10⁶ J
Let radius of flywheel be r .
volume of flywheel = π r² x t where t is thickness
= 3.14 x r² x .113 m³
= .04 r² m³
mass = volume x density
= .04 r² x 7800 = 312.73 r²kg
moment of inertia I = 1 / 2 mass x radius²
= .5 x 312.73 r² x r²
= 156.37 r⁴ kg m²
angular velocity ω = 2π x 93/60
= 9.734 rad /s
kinetic energy = 1/2 Iω² where ω is angular velocity
= .5 x 156.37 r⁴ x 9.734²
= 7408.08 r⁴
Given
7408.08 r⁴ = 14.1 x 10⁶
r⁴ = .19 x 10⁴
r = .66 x 10
= 6.60 m .
Diameter = 13.2 m
b )
centripetal acceleration of a point on its rim = ω² r
= 9.734² x 6.6
= 625.35 m /s²
Answer:
10 GHz
Explanation:
Applying,
v = λf.................... Equation 1
Where v = speed of microwave, λ = wavelength, f = frequency.
make f the subject of the equation
f = v/λ................ Equation 2
Note: Microwave is an electromagnetic wave, and all electromagnetic wave have the same speed, which is 3×10⁸ m/s
From the question,
Given: λ = 3 cm = 0.03 m
Constant; v = 3×10⁸ m/s
Substitute these values into equation 2
f = 3×10⁸/(0.03)
f = 10¹⁰ Hz
f = (10¹⁰/10⁹) GHz
f = 10 GHz
Answer:
Ф = 2.179 eV
Explanation:
This exercise has electrons ejected from a metal, which is why it is an exercise on the photoelectric effect, which is explained assuming the existence of energy quanta called photons that behave like particles.
E = K + Ф
the energy of the photons is given by the Planck relation
E = h f
we substitute
h f = K + Ф
Ф= hf - K
the speed of light is related to wavelength and frequency
c = λ f
f = c /λ
Φ =
let's reduce the energy to the SI system
K = 0.890 eV (1.6 10⁻¹⁹ J / 1eV) = 1.424 10⁻¹⁹ J
calculate
Ф = 6.63 10⁻³⁴ 3 10⁸/405 10⁻⁹ -1.424 10⁻¹⁹
Ф = 4.911 10⁻¹⁹ - 1.424 10⁻¹⁹
Ф = 3.4571 10⁻¹⁹ J
we reduce to eV
Ф = 3.4871 10⁻¹⁹ J (1 eV / 1.6 10⁻¹⁹ J)
Ф = 2.179 eV
The average speed of the car for the entire trip can be calculate by using:

where S is the total distance covered by the car, and t is the total time taken.
The total distance travelled by the car is:

while the total time taken is:

so, the average speed of the car is:

so, the correct answer is (3) 85 km/h.