The resultant vector is 5.2 cm at a direction of 12⁰ west of north.
<h3>
Resultant of the two vectors</h3>
The resultant of the two vectors is calculated as follows;
R = a² + b² - 2ab cos(θ)
where;
- θ is the angle between the two vectors = 45° + (90 - 57) = 78⁰
- a is the first vector
- b is the second vector
R² = (3.7)² + (4.5)² - (2 x 3.7 x 4.5) cos(78)
R² = 27.02
R = 5.2 cm
<h3>Direction of the vector</h3>
θ = 90 - 78⁰
θ = 12⁰
Thus, the resultant vector is 5.2 cm at a direction of 12⁰ west of north.
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Answer-3
Answer:
1.21m
Explanation:
If two speakers are generating a frequency of 280Hz, the smallest separation distance between the speakers that will produce destructive interference at a listener standing in front of them is also known as the wavelength of the sound wave generated.
Using the expression;
Velocity v = frequency f × wavelength ¶
Given frequency = 280Hz, speed of sound v = 338m/s
Substituting this data's in the expression given to get the wavelength will give;
¶ = v/f
¶ = 338/280
¶ = 1.21m
The smallest separation between the speakers that will produce the interference is 1.21m