Find x-component of vector d=(110m , 46 degrees below + x-axis).
Find y-component of vector d=(110m ,46 degrees below + x-axis).
Find x-component of vector v=(350m/s , 28degrees above + x-axis).
Find y-component of vector v=(350 , 28 above + x-axis).
Find x-component of vector a=(9.0 , - y-direction).
Find y-component of vector a=(9.0 , - y-direction).
d(x)=dcos46⁰=110•cos46⁰=76.4 m.
d(y) =- dsin46⁰=- 110•sin46⁰= - 79.1 m.
v(x) = vcos28⁰=350•cos28⁰= 309 m/s
v(y) = vsin28⁰=350•sin28⁰=164.3 m/s
a(x) = 0
a(y) = - 9 m/s²
To find the x-component of a vector, you can use the formula: x = magnitude * cos(angle)
To find the y-component of a vector, you can use the formula: y = magnitude * sin(angle)
Let's calculate each component using the given information:
1. For vector d=(110m , 46 degrees below + x-axis):
The x-component is calculated as:
x = 110m * cos(46 degrees) = 110m * cos(46°) = 74.38 m (rounded to two decimal places)
The y-component is calculated as:
y = 110m * sin(46 degrees) = 110m * sin(46°) = 77.75 m (rounded to two decimal places)
2. For vector v=(350m/s , 28 degrees above + x-axis):
The x-component is calculated as:
x = 350m/s * cos(28 degrees) = 350m/s * cos(28°) = 305.94 m/s (rounded to two decimal places)
The y-component is calculated as:
y = 350m/s * sin(28 degrees) = 350m/s * sin(28°) = 160.79 m/s (rounded to two decimal places)
3. For vector a=(9.0 , - y-direction):
The x-component is given as 9.0 and remains the same.
The y-component is given as - y-direction, indicating that it points in the negative y-direction. Therefore, the y-component is -9.0.
To find the x-component of a vector, you can use trigonometry and the given angle. The formula to find the x-component of a vector is:
x-component = magnitude * cos(angle)
For vector d:
x-component of d = 110m * cos(46 degrees)
x-component of d = 110m * cos(46°)
x-component of d ≈ 75.547m
For vector v:
x-component of v = 350m/s * cos(28 degrees)
x-component of v ≈ 307.118m/s
For vector a:
The x-component of a is given as 9.0, so there is no need to calculate it since it is already provided.
To find the y-component of a vector, you can again use trigonometry and the given angle, but this time you will use the sine function. The formula to find the y-component of a vector is:
y-component = magnitude * sin(angle)
For vector d:
y-component of d = 110m * sin(46 degrees)
y-component of d ≈ 78.954m
For vector v:
y-component of v = 350m/s * sin(28 degrees)
y-component of v ≈ 161.065m/s
For vector a:
The y-component of a is given as -y-direction, which means it is pointing down in the negative y-axis direction. Therefore, the y-component of a is -9.0.