Help me with magnitude and direction?

In summary, the question is asking for the magnitude and direction of the vectors a+b and b-a. Using the SOHCAHTOA method, we can find the magnitude of a+b to be 8.07 m and the direction to be 46° east of north. For b-a, the magnitude is 1.46 m and the direction is 56° west of south.
  • #1
mikeyp
1
0

Homework Statement




Vector a has a magnitude of 4.3 m and is directed east. Vector b has a magnitude of 3.9 m and is directed 35° west of north. What are (a) the magnitude and (b) the direction (from east) of a + b ? What are (c) the magnitude and (d) the direction (from east) of b - a? Round your angles to the nearest degree.


Homework Equations


socahtoa? a^2+b^2=c^2
sin(35)*3.9/4.3


The Attempt at a Solution


sin(35)*3.9/4.3
 
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  • #2
mikeyp said:

Homework Statement




Vector a has a magnitude of 4.3 m and is directed east. Vector b has a magnitude of 3.9 m and is directed 35° west of north. What are (a) the magnitude and (b) the direction (from east) of a + b ? What are (c) the magnitude and (d) the direction (from east) of b - a? Round your angles to the nearest degree.


Homework Equations


socahtoa? a^2+b^2=c^2
sin(35)*3.9/4.3


The Attempt at a Solution


sin(35)*3.9/4.3

Welcome to the PF,

On vector questions like this, it is helpful to draw a diagram showing the vectors and their addition/subtraction. Can you draw the diagrams and scan/upload them?
 

1. What is magnitude and direction in science?

Magnitude and direction are two important concepts in science, particularly in the field of physics. Magnitude refers to the size or amount of a quantity, while direction refers to the orientation or path of movement. Together, they describe the overall intensity or force of a physical quantity.

2. How do you calculate the magnitude and direction of a vector?

To calculate the magnitude and direction of a vector, you can use the Pythagorean theorem and trigonometric functions. The magnitude of a vector is found by taking the square root of the sum of the squared values of its components. To find the direction, you can use inverse trigonometric functions to determine the angle between the vector and a reference axis.

3. What is the difference between magnitude and magnitude and direction?

Magnitude and direction are two distinct concepts, with magnitude referring to the size or amount of a quantity, while direction refers to the orientation or path of movement. Together, they describe the overall intensity or force of a physical quantity, but they are not interchangeable terms.

4. How is magnitude and direction used in real-world applications?

Magnitude and direction are used in various real-world applications, such as navigation, engineering, and astronomy. For example, in navigation, the magnitude and direction of a vector can be used to determine the speed and direction of a moving object. In engineering, they are used to calculate forces and design structures. In astronomy, they are used to track the movement of celestial bodies.

5. What are some common units for measuring magnitude and direction?

The units for measuring magnitude and direction depend on the specific physical quantity being measured. For example, the magnitude of a force is typically measured in newtons (N), while the direction is measured in degrees (°) or radians (rad). Other common units for magnitude and direction include meters per second (m/s) for velocity, kilograms (kg) for mass, and joules (J) for energy.

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