Vector L is 303 m long in a
1 answer:
Answer:
584.32m
Explanation:
Firstly, we need to find the x and y components of each vector.
x-component for vector L=303cos205°=-274.61
y-component for vector L=303sin205°=-128.05
x-component for vector M=555cos105°=-143.64
y-component for vector M=555sin105°=536.09
Since it's the vector sum, we add the x and y components of each vector.
Resultant vector x-component -274.61+(-143.64)=-418.25
Resultant vector y-component -128.05+536.09=408.04
Now, to find the magnitude, we use the formula
sqrt(-418.25^2+408.04^2)=584.32m
Check my work for errors just in case.
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Answer:
r₂ = 0.316 m
Explanation:
The sound level is expressed in decibels, therefore let's find the intensity for the new location
β = 10 log
let's write this expression for our case
β₁ = 10 log \frac{I_1}{I_o}
β₂ = 10 log \frac{I_2}{I_o}
β₂ -β₁ = 10 ( )
β₂ - β₁ = 10
log \frac{I_2}{I_1} = = 3
= 10³
I₂ = 10³ I₁
having the relationship between the intensities, we can use the definition of intensity which is the power per unit area
I = P / A
P = I A
the area is of a sphere
A = 4π r²
the power of the sound does not change, so we can write it for the two points
P = I₁ A₁ = I₂ A₂
I₁ r₁² = I₂ r₂²
we substitute the ratio of intensities
I₁ r₁² = (10³ I₁ ) r₂²
r₁² = 10³ r₂²
r₂ = r₁ / √10³
we calculate
r₂ =
r₂ = 0.316 m