Answer:
the required solution is; x(t) = 0.675<em>sin</em>( 2.222t )
Explanation:
Given the data in the question;
Using both Newton's and Hooke's law;
m + k = 0, (0) = 0, (0) = 1.5
given that mass m = 9 kg
= 1.8 m
k is F / x
hence
k = F / x
given that, F = 80 N
we substitute
k = 80 / 1.8
k = 44.44
so
m + k = 0,
we input
9 + 44.44 = 0,
+ 4.9377 = 0
so auxiliary equation is,
r² + 4.9377 = 0
r² = -4.9377
r = √-4.9377
r = ±2.222i
hence, the solution will be;
x(t) = A×cos( 2.222t ) + B×sin( 2.222t )
⇒ (t) = -2.222Asin( 2.222t ) + 2.222Bcos( 2.222t )
using initial conditions
x(0) = 0
⇒ 0 = A
(t) = 1.5
1.5 = 2.222B
so
B = 1.5 / 2.222 = 0.675
Hence, the required solution is; x(t) = 0.675<em>sin</em>( 2.222t )
To solve this problem it is necessary to apply the concepts related to the described wavelength through frequency and speed. Mathematically it can be expressed as:
Where,
Wavelength
f = Frequency
v = Velocity
Our values are given as,
Speed of sound
Keep in mind that we do not use the travel speed of the ambulance because we are in front of it. In case it approached or moved away we should use the concepts related to the Doppler effect:
Replacing we have,
Therefore the frequency that you hear if you are standing in from of the ambulance is 0.1214m
d=18cm=0.18m thickness of board
vi=420m/s speed before entering the board
vf=320m/s speed when leaving the board
vf²=vi²+2×a×d
Acceleration a=(vf²-vi²)/2/d
a=-205.5m/s².
As expected, a is negative because the bullet is decelerated.
vf=vi+a×t
t=(vf-vi)/a=(320-420)/(-205.5)= 100/205.5=0.486s
t=0.486s=486ms
Answer:
-775 rad/s^2
Explanation:
Knowing the initial and final angular speed is and , respectively. We can use the following formula for equation of motion to calculate the average angular acceleration in t = 0.569 seconds
D evaporation is the correct answer