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 given vector, you can use trigonometry. The formula for finding the x-component is:
x-component = magnitude * cos(angle)
1. For vector d:
Magnitude = 110m
Angle = 46 degrees below the +x-axis. To find the angle relative to the +x-axis, subtract 46 degrees from 180 degrees (since it's below the x-axis).
Angle = 180 degrees - 46 degrees = 134 degrees
x-component of vector d = 110m * cos(134 degrees)
2. For vector v:
Magnitude = 350m/s
Angle = 28 degrees above the +x-axis.
x-component of vector v = 350m/s * cos(28 degrees)
3. For vector a:
Magnitude = 9.0
Angle is in the -y direction, so its x-component will be zero.
x-component of vector a = 0
To find the y-component of a given vector, you can again use trigonometry. The formula for finding the y-component is:
y-component = magnitude * sin(angle)
1. For vector d:
y-component of vector d = 110m * sin(134 degrees)
2. For vector v:
y-component of vector v = 350m/s * sin(28 degrees)
3. For vector a:
y-component of vector a = -9.0