A runner first runs a displacement A of 3.30 km due south, and then a second displacement B that points due east. The magnitude of the resultant displacement A + B is 5.27 km. What is the magnitude (in m) of B? What is the angle that A + B makes relative to due south? (Your answer must be a positive number from 0 to 180 degrees).

A runner first runs a displacement A of 3.30 km due south, and then a second displacement B that points due east. The magnitude of the resultant displacement A + B is 5.27 km. What is the magnitude (in m) of B? What is the angle that A + B makes relative to due south? (Your answer must be a positive number from 0 to 180 degrees).

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section: Chapter Questions

Problem 45P

See similar textbooks

Similar questions

Three displacement vectors of a croquet ball are shown in Figure P1.44, where |A|=20.0units, |B|=40.0units, and |C|=30.0units. Find (a) the resultant in unit-vector notation and (b) the magnitude and direction of the resultant displacement. Figure P1.44
Vector A has x and y components of 8.70 cm and 15.0 cm, respectively; vector B has x and y components of 13.2 cm and 6.60 cm, respectively. If AB+3C=0, what are the components of C?
A skater glides along a circular path of radius 5.00 m in clockwise direction. ‘When he coasts around one- half of the circle, starting from the west point, find (a) the magnitude of his displacement vector and (b) how far he actually skated. (c) What is the magnitude of his displacement vector when he skates all the way around the circle and comes back to the west point?
Find the horizontal and vertical components of the 100-m displacement of a superhero who flies from the top of a tall building following the path shown in Figure P1.40. Figure P1.40
The magnitudes of two vectors A and B are 12 units and 8 units, respectively. What are the largest and smallest possible values for the magnitude of the resultant vector R = A + B? (a) 14.4 and 4 (b) 12 and 8 (c) 20 and 4 (d) none of these.
A vector points from the origin into the second quadrant of the xy plane. What can you conclude about its components? (a) Both components are positive. (b) The x component is positive, and the y component is negative. (c) The x component is negative, and the y component is positive. (d) Both components are negative. (e) More than one answer is possible.
Figure OQ1.13 shows two vectors D1 and D2. Which of the possibilities (a) through (d) is the vector D22D1, or (e) is it none of them? Figure OQ1.13
If A + B = 0, the corresponding components of the two vectors Aand Bmust be (a) equal, (b) positive, (c) negative, (d) of opposite sign.
Consider the three displacement vectors A=(3i3j)m, B=(i4j)m, and C=(2i+5j)m. Use the component method to determine (a) the magnitude and direction of the vector D=A+B+C and (b) the magnitude and direction of E=AB+C.
What is the y component of the vector shown in Figure OQ3.9? (a) 3 cm (b) 6 cm (c) 4 cm (d) 6 cm (e) none of those answers
A hiker walks from (x1, y1) = (4.00 km. 3.00 km) to (x2, y2) = (3.00 km, 6.00 km), (a) What distance has the traveled? (b) The hiker desires to return to his starting point. In what direction should he go? (Give the angle with respect to due cast.) (See Sections 3.2 and 3.3.)
A commuter airplane starts from an airport and takes the route shown in Figure P1.71. The plane first flies to city A, located 175 km away in a direction 30.0 north of east. Next, it flies for 150. km 20.0 west of north, to city B. Finally, the plane flies 190. km due west, to city C. Find the location of city C relative to the location of the starting point. Figure P1.71