Answer:
Appliances or Lights (c)
Explanation:
They use voltage for functionality
Answer:
Speed, v = 5 m/s
Explanation:
We have,
The length of the football field, l = 100 m
A person takes 20 seconds to run its length.
It is required to find the speed of the person with which he should run. The distance covered divided by time taken is called its velocity.
So, the speed of the person is 5 m/s.
A) change in ht after 180m = 180 * sin(4-deg.) = 12.56m
net work done by gravity on the cyclist = mass * gravity * height diff.
= 85 * 9.8 * 12.56
= 10470J
= 10.5kJ
B) Kinetic energy = 1/2 * mass * vel.^2 = work done by gravity = 10470J
vel.^2 = 10470 * 2 / 85 = 246.4
vel. = 15.7m/s
Quasi frequency = 4√6
Quasi period = π√6/12
t ≈ 0.4045
<u>Explanation:</u>
Given:
Mass, m = 20g
τ = 400 dyn.s/cm
k = 3920
u(0) = 2
u'(0) = 0
General differential equation:
mu" + τu' + ku = 0
Replacing the variables with the known value:
20u" + 400u' + 3920u = 0
Divide each side by 20
u" + 20u' + 196u = 0
Determining the characteristic equation by replacing y" with r², y' with r and y with 1 in the differential equation.
r² + 20r + 196 = 0
Determining the roots:
r = -10 ± 4√6i
The general solution for two complex roots are:
y = c₁ eᵃt cosbt + c₂ eᵃt sinbt
with a the real part of the roots and b be the imaginary part of the roots.
Since, a = -10 and b = 4√6
u(t) = c₁e⁻¹⁰^t cos 4√6t + c₂e⁻¹⁰^t sin 4√6t
u(0) = 2
u'(0) = 0
(b)
Quasi frequency:
μ =
(c)
Quasi period:
T = 2π / μ
(d)
|u(t)| < 0.05 cm
u(t) = |2e⁻¹⁰^t cos 4√6t + 5√6/6 e⁻¹⁰^t sin 4√6t < 0.05
solving for t:
τ = t ≈ 0.4045