Vector A has magnitude of 6.0 at an angle of 50.0 o from the x-axis. Vector B has magnitude of 12.0 at an angle of -10.0 o from the x-axis. Let C=A+B. Let D=A-B. Let V=2*A-B.
What is the x-component of vector C?
What is the y-component of vector C?
What is the x-component of vector D?
What is the y-component of vector D?
What is the x-component of vector V?
What is the y-component of vector V?
Components Vector Sum Difference?
2020-09-22 1:33 pm
回答 (1)
2020-09-22 1:57 pm
Vector A = 6.0 cos50° i + 6.0 sin50° j
Vector B = 12.0 cos(-10°) i + 12.0 sin(-10°) j
Vector B = 12.0 cos10° i - 12.0 sin10° j
Vector C = Vector A + Vector B
Vector C = (6.0 cos50° i + 6.0 sin50° j) + (12.0 cos10° i - 12.0 sin10° j)
Vector C = (6.0 cos50° + 12.0 cos10°) i + (6.0 sin50° - 12.0 sin10°) j
Vector D = Vector A - Vector B
Vector D = (6.0 cos50° i + 6.0 sin50° j) - (12.0 cos10° i - 12.0 sin10° j)
Vector D = (6.0 cos50° - 12.0 cos10°) i + (6.0 sin50° + 12.0 sin10°) j
Vector V = 2 × Vector A - Vector B
Vector V = 2 × (6.0 cos50° i + 6.0 sin50° j) - (12.0 cos10° i - 12.0 sin10° j)
Vector V = (12.0 cos50° - 12.0 cos10°) i + (12.0 sin50° + 12.0 sin10°) j
The answers:
The x-component of Vector C = 6.0 cos50° + 12.0 cos10° ≈ 15.7
The y-component of Vector C = 6.0 sin50° - 12.0 sin10° ≈ 2.5
The x-component of Vector D = 6.0 cos50° - 12.0 cos10° ≈ -8.0
The y-component of Vector D = 6.0 sin50° + 12.0 sin10° ≈ 6.7
The x-component of Vector D = 12.0 cos50° - 12.0 cos10° ≈ -4.1
The y-component of Vector D = 12.0 sin50° + 12.0 sin10° ≈ 11.3
Vector B = 12.0 cos(-10°) i + 12.0 sin(-10°) j
Vector B = 12.0 cos10° i - 12.0 sin10° j
Vector C = Vector A + Vector B
Vector C = (6.0 cos50° i + 6.0 sin50° j) + (12.0 cos10° i - 12.0 sin10° j)
Vector C = (6.0 cos50° + 12.0 cos10°) i + (6.0 sin50° - 12.0 sin10°) j
Vector D = Vector A - Vector B
Vector D = (6.0 cos50° i + 6.0 sin50° j) - (12.0 cos10° i - 12.0 sin10° j)
Vector D = (6.0 cos50° - 12.0 cos10°) i + (6.0 sin50° + 12.0 sin10°) j
Vector V = 2 × Vector A - Vector B
Vector V = 2 × (6.0 cos50° i + 6.0 sin50° j) - (12.0 cos10° i - 12.0 sin10° j)
Vector V = (12.0 cos50° - 12.0 cos10°) i + (12.0 sin50° + 12.0 sin10°) j
The answers:
The x-component of Vector C = 6.0 cos50° + 12.0 cos10° ≈ 15.7
The y-component of Vector C = 6.0 sin50° - 12.0 sin10° ≈ 2.5
The x-component of Vector D = 6.0 cos50° - 12.0 cos10° ≈ -8.0
The y-component of Vector D = 6.0 sin50° + 12.0 sin10° ≈ 6.7
The x-component of Vector D = 12.0 cos50° - 12.0 cos10° ≈ -4.1
The y-component of Vector D = 12.0 sin50° + 12.0 sin10° ≈ 11.3
收錄日期: 2021-04-24 08:04:01
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