Answer:
θ = 30⁰
Explanation:
We have been given two wave displacement equations,
........(1)
........(2)
The waves will have same displacements when
(say)
Therefore, operating (2) - (1), we get,

or,
(since, sin 30⁰ = 0.5)
We can check the answer by putting
in equations (1) and (2),


Answer:
a. 0.143 mm b. 77.6 rad/m c. 483.18 rad/s d. +1
Explanation:
a. ym
Since the amplitude is 0.143 mm, ym = amplitude = 0.143 mm
b. k
We know k = wave number = 2π/λ where λ = wavelength.
Also, λ = v/f where v = speed of wave in string = √(T/μ) where T = tension in string = 19.3 N and μ = mass per unit length = 5.12 g/cm = 5.12 ÷ 1000 kg/(1 ÷ 100 m) = 0.512 kg/m and f = frequency = 76.9 Hz.
So, λ = v/f = √(T/μ)/f
substituting the values of the variables into the equation, we have
λ = √(T/μ)/f
= √(19.6 N/0.512 kg/m)/76.9 Hz
= √(38.28 Nkg/m)/76.9 Hz
= 6.187 m/s ÷ 76.9 Hz
= 0.081 m
= 81 mm
So, k = 2π/λ
= 2π/0.081 m
= 77.6 rad/m
c. ω
ω = angular frequency = 2πf where f = frequency of wave = 76.9 Hz
So, ω = 2πf
= 2π × 76.9 Hz
= 483.18 rad/s
d. The correct choice of sign in front of ω?
Since the wave is travelling in the negative x - direction, the sign in front of ω is positive. That is +1.
Answer:
Eleven seconds.
Explanation:
Two keys are needed to solve this problem. First, the conservation of momentum: allowing you to calculate the cart's speed after the elephant jumped onto it. It holds that:

So, once loaded with an elephant, the cart was moving with a speed of 4.29m/s.
The second key is the kinematic equation for accelerated motion. There is one force acting on the cart, namely friction. The friction acts in the opposite direction to the horizontal direction of the velocity v0, its magnitude and the corresponding deceleration are:

The kinematic equation describing the decelerated motion is:

It takes 11 seconds for the comical elephant-cart system to come to a halt.
Answer:
Heat, Let me explain,
Explanation:
An exothermic reaction is like... Lighting a candle so it produces a small amount of heat in less than a second and then normal heat.