2 displacement vectors of 15 meters and 10 meters are combined.
a.Find the magnitude of the minimum possible resultant and the angle between the vectors.
b. Find the magnitude of the maximum possible resultant and the angle between the vectors.
Isn't the maximum when they point the same direction? The minimum when they point opposite directions?
I will be happy to critique your thinking.
To find the minimum and maximum possible resultant vectors, we can combine the given displacement vectors using vector addition. The resultant vector will represent the total displacement achieved by combining the two vectors.
a. Minimum Possible Resultant:
To find the minimum possible resultant, we need to subtract one vector from the other. Let's subtract the vector of 10 meters from the vector of 15 meters. The resultant will be the vector connecting the end point of the second vector to the end point of the first vector.
To subtract vectors, we can reverse the direction of the vector we want to subtract and then add the reversed vector to the other vector. In this case, we want to subtract the vector of 10 meters from the vector of 15 meters.
15 meters - 10 meters = 15 meters + (-10 meters)
Since these vectors are in a straight line, we can simply add their magnitudes:
15 meters + (-10 meters) = 5 meters
Therefore, the magnitude of the minimum possible resultant is 5 meters.
To find the angle between the vectors, we can use trigonometry. Since the vectors are in a straight line, the angle between them is 180 degrees.
b. Maximum Possible Resultant:
To find the maximum possible resultant, we need to add the two vectors together. The resultant will be the vector connecting the start point of the first vector to the end point of the second vector.
To add vectors, we can simply add their magnitudes and consider their directions:
15 meters + 10 meters = 25 meters
Therefore, the magnitude of the maximum possible resultant is 25 meters.
To find the angle between the vectors, we can use trigonometry. Since the vectors are in a straight line, the angle between them is 0 degrees.
In summary:
a. The magnitude of the minimum possible resultant is 5 meters and the angle between the vectors is 180 degrees.
b. The magnitude of the maximum possible resultant is 25 meters and the angle between the vectors is 0 degrees.