Concept explainers
A person going for a walk follows the path shown in Figure P1.51. The total trip consists of four straight-line paths. At the end of the walk, what is the person’s resultant displacement measured from the starting point?
Figure P1.51
The person’s resultant displacement and the direction in the starting point.
Answer to Problem 51P
The person’s resultant displacement in the starting point is
Explanation of Solution
The following figure shows the person going a walk follows the path.
The person going for a walk in the first straight path is
The person going for a second straight line path is
Write the expression for third path of the person moves in x and y component.
Here,
Write the expression for fourth path of the person moves in x and y component.
Here,
Write the expression for net displacement vectors.
Here,
Write the expression for the magnitude of the resultant displacement.
Here,
Write the expression for the direction of the displacement.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Therefore, the person’s resultant displacement in the starting point is
Want to see more full solutions like this?
Chapter 1 Solutions
Principles of Physics: A Calculus-Based Text
- 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 P1.44arrow_forwardFigure E1.28 y В (15.0 m) D (10.0 m) 30.0° 53.00 25.0° Č (12.0 m) A (8.00 m) 3. Given the vectors on Fig E1.28: a. Find the components of each vector. Express your answers in î , ĵ, and k notation.arrow_forwardFor the triangle shown in Figure P1.45, what are (a) thelength of the un known side, (b) the tangent of θ, and (c) thesine of ϕ?arrow_forward
- Suppose you went for a drive along a long, straight road that runs east-west. Let's define east to be the positive x direction. From your home, you drive east at 30. mi/hr to your friends house for 20. minutes, then at 48 mi/hr east for 10. minutes to the grocery store. Finally, you drive west at 60. mi/hr without stopping to get home. How many minutes will it take to drive from the grocery store to your home (at 60. mi/hr)? Note: Your answer should have the correct number of significant figuresarrow_forwardA man leaves his front door, walks 1000 ft east, 2000 ft north, and then takes a penny from his pocket and drops it from a cliff 500 ft Set up a coordinate system and write down an expression, using unit vectors, for the displacement of the The man then returns to his front door, following a different path on the return trip. What is his resultant displacement for the round trip?arrow_forwardA surveyor measures the distance across a straight river by the following method: Starting directly across from a tree on the opposite bank, he walks x = 100 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline to the tree is θ = 35.0° (Fig. P1.49). How wide is the river?arrow_forward
- Q1.23 Consider the two repeated vector products A × (B × C) and (Ả × B) × Č. Give an example that illustrates the general rule that these two vector products do not have the same magni- tude or direction. Can you choose the vectors Á, B, and Ć such that these two vector products are equal? If so, give an example.arrow_forwardA teenager walks 191 meters north to their friends house and gets therelin 5 min. They forgot their phone so they run back to there house and return to there friends house in 9.8 minutes. If north is considered positive and south is considered negative, what is the total distance of the teenage when they return to their friend's house from the beginning of the trip?arrow_forward71. 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. t 1 y (km) 250 E N C W E 200 20.0° 150 R 100 110° a 50 30.0° x (km) 50 100 150 200 Figure P1.71arrow_forward
- The vector from figure E1.28 Are 164.375° and 19°arrow_forwardFor the triangle shown in Figure P1.45, what are (a) the length of the unknown side, (b) the tangent of θ, and (c) the sine of Φ?arrow_forward5.00 cars pass through an intersection each second. How many cars pass the intersection in 1.00 year? There are 365.25 days in one year. Write your answer with the correct number of significant figures.arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning