Question

Find the resultant of the following vectors: Vector A, magnitude 7, right direction; vector B, magnitude 5, right direction.

A) 7 right
B) 12 left
C) 12 right
D) 2 right

A woman walks 6 km to the north to a bank, then 2 km south to a grocery store, find her resultant displacement.
A) 8 km north
B) 12 km north
C) 4 km north
D) 4 km south

A woman walks from her house 6 km to the north to a bank, then 2 km south to a grocery store, then she returns home. Find her resultant displacement.
A) 12 km
B) 8 km
C) 0 km
D) 4 km south

A train is going down the tracks toward the south at 50 mph. Two passengers, A and B, are sitting next to each other in Row 7. Relative to a person standing next to the tracks, Passenger A is
A) moving 50 mph
B) not moving
C) cannot answer with information given
D) moving more than 50 mph

A woman walks 6 km to the north to a bank, then 2 km south to a grocery store, find her distance walked.
A) 6 km
B) 12 km
C) 4 km
D) 8 km

Find the resultant of the following vectors: Vector A, magnitude 7, left direction; vector B, magnitude 5, right direction.
A) 2 left
B) 12 left
C) 12 right
D) 2 right

A train is going down the tracks toward the south at 50 mph. Two passengers, A and B, are sitting next to each other in Row 7. Relative to passenger B, passenger A is
A) moving 50 mph
B) not moving
C) cannot answer with information given
D) moving more than 50 mph

Answer 1

The resultants for given vector scenarios, such as combinations of magnitude and direction, follow the rules of vector addition and subtraction. They can be computed by summing magnitudes for parallel vectors or by determining the difference for vectors in opposing directions.

Step-by-step explanation:

To find the resultant of two vectors moving in the same direction, you simply add their magnitudes. Therefore, Vector A, with a magnitude of 7 in the right direction, combined with Vector B, with a magnitude of 5 in the right direction, results in a vector with a magnitude of 12 in the right direction, which is option C) 12 right.

The resultant displacement of a person who walks 6 km north and then 2 km south is 4 km to the north, since the north and south displacements partially cancel each other out. This is option C) 4 km north.

If the woman returns home after her trip to the bank and the grocery store, her total displacement is 0 km because she ends up where she started, which is option C) 0 km.

A passenger on a train moving south at 50 mph, relative to a person standing next to the tracks, is moving at 50 mph in the same direction as the train. This is option A) moving 50 mph.

The total distance walked by the woman who walks 6 km north and then 2 km south is the sum of both distances, which equals 8 km, option D) 8 km.

For vectors of opposite direction on a straight line, such as Vector A with a magnitude of 7 pointing left and Vector B with a magnitude of 5 pointing right, the resultant vector has a magnitude equal to the numerical difference between the two, and its direction is the same as the direction of the larger vector. The magnitude of the resultant is 2 and its direction is left, which is option A) 2 left.

Relative to Passenger B, Passenger A is not moving because both are sitting next to each other in the train and relative motion is zero. This is option B) not moving.