![]() (It is in the fourth quadrant because 309 degrees lies between 270 degrees or due South and 360 degrees or due East.) For communication sake, we will refer to the first displacement as A and the second displacement as B. The first displacement is due South and the resulting displacement (at 309 degrees) is somewhere in the fourth quadrant. Like the previous problem (and most other problems in physics), this problem is best approached using a diagram. Determine the magnitude and direction of the second leg of the trip. The overall displacement of the two-legged trip is 19.7 km at 309 degrees. The hiker then makes a turn towards the southeast and finishes at the final destination. Vector Addition || Vector Components || Vector Resolutionĥ8. This is the angle which the resultant makes with the original line of motion (the 36.7 ft displacement vector). tangent(theta) = opposite/adjacent = (17.0 ft) / (44.9 ft) The angle theta in the diagram above can be found using the tangent function. Since these displacement vectors are at right angles to each other, the magnitude of the resultant can be determined using the Pythagorean theorem. These two vectors can be added together and the resultant can be drawn from the starting location to the final location. Now it is obvious from the diagram on the right that the three displacement vectors are equivalent to two perpendicular displacement vectors of 44.9 feet and 17 feet. Since the three displacements could be done in any order without effecting the resulting displacement, these three legs of the trip are conveniently rearranged in the diagram below on the right. The three displacements are shown in the diagram below on the left. This problem is best approached using a diagram of the physical situation. (b) Determine the direction of the displacement vector relative to the original line of motion.Īnswer: (a) 48.0 feet (b) 21 degrees from the original line of motion (a) Determine the magnitude of the overall displacement. Finally, she turns right and walks 8.2 feet to a final destination. She then turns left and walks 17.0 feet straight ahead. In a grocery store, a shopper walks 36.7 feet down an aisle. So the direction is 7.59 degrees short of 180 degrees. Directions of vectors are expressed as the counterclockwise angle of rotation relative to east. ![]() This angle theta is the angle between west and the resultant. tangent(theta) = opposite/adjacent = (4.0 m) / (30.0 m) ![]() A non-scaled sketch is useful for visualizing the situation.Īpplying the Pythagorean theorem leads to the magnitude of the resultant (R). The resultant of these two displacements can be found using the Pythagorean theorem (for the magnitude) and the tangent function (for the direction). The series of five displacements is equivalent to two displacements of 30 meters, West and 4 meters, North. Vertical: 12.0 meters, North 8.0 meters, South = 4.0 meters, North Horizontal: 2.0 meters, West 31.0 meters, West 3.0 meters, East = 30.0 meters, West The first step is to determine the sum of all the horizontal (east-west) displacements and the sum of all the vertical (north-south) displacements. To insure the most accurate solution, this problem is best solved using a calculator and trigonometric principles. Using either a scaled diagram or a calculator, determine the magnitude and direction of Anna's resulting displacement. In the Vector Addition Lab, Anna starts at the classroom door and walks: Vectors and Projectiles - Home || Printable Version || Questions and LinksĪnswers to Questions: All || #1-9 || #10-45 || #46-55 || #56-72ĥ6. When we use the kinematic equations, we use specific notation to denote initial and final measurements.įor example, when we have an initial velocity value, it is written as $ \Large\mathcal = \large 5.1 \textrm m $Ģ.) You and your partner disagree about whether or not you can make a picket fence drop to the ground in exactly 1.0 s.The Review Session » Vectors and Projectiles » Answers Q#56-72 Vectors and Projectiles To keep our focus on high school physics, we will not be covering integrals. Kinematics equations require knowledge of derivatives, rate of change, and integrals. ![]() The kinematic equations are a set of equations that describe the motion of an object with constant acceleration. ![]()
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