Final answer:
To represent different velocities and displacements using vectors, you need to set up proportions based on the given information. Adding two vectors graphically can be done using the tail-to-tip method. When graphically adding vectors, you can move, rotate, or change the length of the vectors without affecting the final result.
Step-by-step explanation:
1. To find out how long you should draw a vector to represent a velocity of 20 m/s, you need to set up a proportion using the given information. Since the length of the vector is directly proportional to the magnitude of the velocity, you can set up the proportion as:
15 mm / 30 m/s = x mm / 20 m/s
Cross multiplying and solving for x, you get:
x = 10 mm
Therefore, you should draw a vector 10 mm long to represent a velocity of 20 m/s.
2. Similar to the first question, you can set up a proportion using the given information. The displacement is directly proportional to the length of the vector, so you can set up the proportion as:
1 cm / 5 km = 3 cm / x km
Cross multiplying and solving for x, you get:
x = 15 km
Therefore, a 3 cm vector represents a displacement of 15 km.
3. To add two vectors graphically, you can use the tail-to-tip method. Place the tail of the second vector at the tip of the first vector, and draw the resultant vector from the tail of the first vector to the tip of the second vector. This resultant vector represents the sum of the two vectors.
4. When graphically adding one vector to another, you are allowed to move the vector, rotate the vector, and change the vector's length. These actions do not affect the final result as long as the relative positions and directions of the vectors are maintained.
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