A jogger travels a route that has two parts. The first is a displacement A → of 2.50 km due south, and the second involves a displacement B → that points due east. (a) The resultant displacement A → + B → has a magnitude of 3.75 km. What is the magnitude of B → , and what is the direction of A → + B → relative to due south? (b) Suppose that A → − B → had a magnitude of 3.75 km. What then would be the magnitude of B → , and what is the direction of A → − B → relative to due south?
A jogger travels a route that has two parts. The first is a displacement A → of 2.50 km due south, and the second involves a displacement B → that points due east. (a) The resultant displacement A → + B → has a magnitude of 3.75 km. What is the magnitude of B → , and what is the direction of A → + B → relative to due south? (b) Suppose that A → − B → had a magnitude of 3.75 km. What then would be the magnitude of B → , and what is the direction of A → − B → relative to due south?
Solution Summary: The author calculates the vector diagram by using the Pythagorean theorem of vector addition, where A and B are the two vectors perpendicular to each other.
A jogger travels a route that has two parts. The first is a displacement
A
→
of 2.50 km due south, and the second involves a displacement
B
→
that points due east. (a) The resultant displacement
A
→
+
B
→
has a magnitude of 3.75 km. What is the magnitude of
B
→
, and what is the direction of
A
→
+
B
→
relative to due south? (b) Suppose that
A
→
−
B
→
had a magnitude of 3.75 km. What then would be the magnitude of
B
→
, and what is the direction of
A
→
−
B
→
relative to due south?
Given vector A = <23, -3, 3> and vector B = <0, 18, 15> , what is the magnitude of A x B?
A jogger travels a route that has two parts. The first is a displacement A→ of 3.00 km due south, and the second involves a displacement B→ that points due east. The resultant displacement A→ + B→ has a magnitude of 3.75 km. (a) What is the magnitude of B→, and (b) what is the direction of A→ + B→ as a positive angle relative to due south? Suppose that A→ - B→ had a magnitude of 3.75 km. (c) What then would be the magnitude of B→, and (d) what is the direction of A→ - B→ relative to due south?
A grasshopper makes four jumps. The displacement vectors are (1) 27.0 cm, due west; (2) 23.0 cm, 35o south of west; (3) 28.0 cm, 55o south of east, and (4) 35.0 cm, 63o north of east (5) 18.0 cm, east. Find the magnitude and direction of the resultant displacement. Express the direction of the resultant displacement.
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