![]() ![]() If we can find the components of then we can combine them to solve for its magnitude and direction. The quantity is known, and we are asked to find None of the velocities are perpendicular, but it is possible to find their components along a common set of perpendicular axes. In this problem, somewhat different from the previous example, we know the total velocity and that it is the sum of two other velocities, (the wind) and (the plane relative to the air mass). What is the speed and direction of the wind? An airplane is known to be heading north at 45.0 m/s, though its velocity relative to the ground is 38.0 m/s at an angle west of north. The plane is known to be moving at 45.0 m/s due north relative to the air mass, while its velocity relative to the ground (its total velocity) is 38.0 m/s in a direction west of north. Thus, we can add the two velocities by using the equations and directly.Įxample 2: Calculating Velocity: Wind Velocity Causes an Airplane to DriftĬalculate the wind velocity for the situation shown in Figure 5. Because the boat is directed straight toward the other shore, its velocity relative to the water is parallel to the -axis and perpendicular to the velocity of the river. We start by choosing a coordinate system with its xx-axis parallel to the velocity of the river, as shown in Figure 4. Let us calculate the magnitude and direction of the boat’s velocity relative to an observer on the shore, The velocity of the boat, is 0.75 m/s in the -direction relative to the river and the velocity of the river, is 1.20 m/s to the right. Refer to Figure 4, which shows a boat trying to go straight across the river. What is the total displacement of the boat relative to the shore? The current in the river, however, flows at a speed of 1.20 m/s to the right. A boat attempts to travel straight across a river at a speed 0.75 m/s. The following equations give the relationships between the magnitude and direction of velocity ( and ) and its components ( and ) along the x– and y-axes of an appropriately chosen coordinate system:Įxample 1: Adding Velocities: A Boat on a River Figure 4. We will concentrate on analytical techniques. In two-dimensional motion, either graphical or analytical techniques can be used to add velocities. For example, if a field hockey player is moving at straight toward the goal and drives the ball in the same direction with a velocity of relative to her body, then the velocity of the ball is relative to the stationary, profusely sweating goalkeeper standing in front of the goal. In one-dimensional motion, the addition of velocities is simple-they add like ordinary numbers. How do we add velocities? Velocity is a vector (it has both magnitude and direction) the rules of vector addition discussed in Chapter 3.2 Vector Addition and Subtraction: Graphical Methods and Chapter 3.3 Vector Addition and Subtraction: Analytical Methods apply to the addition of velocities, just as they do for any other vectors. In this module, we first re-examine how to add velocities and then consider certain aspects of what relative velocity means. These situations are only two of many in which it is useful to add velocities. The velocity of the object relative to the observer is the sum of these velocity vectors, as indicated in Figure 1 and Figure 2. In each of these situations, an object has a velocityrelative to a medium (such as a river) and that medium has a velocity relative to an observer on solid ground. The plane does not move relative to the ground in the direction it points rather, it moves in the direction of its total velocity (solid arrow). An airplane heading straight north is instead carried to the west and slowed down by wind. Its total velocity (solid arrow) relative to the shore is the sum of its velocity relative to the river plus the velocity of the river relative to the shore. A boat trying to head straight across a river will actually move diagonally relative to the shore as shown. The plane is moving straight ahead relative to the air, but the movement of the air mass relative to the ground carries it sideways. Similarly, if a small airplane flies overhead in a strong crosswind, you can sometimes see that the plane is not moving in the direction in which it is pointed, as illustrated in Figure 2. The reason, of course, is that the river carries the boat downstream. The boat does not move in the direction in which it is pointed. If a person rows a boat across a rapidly flowing river and tries to head directly for the other shore, the boat instead moves diagonally relative to the shore, as in Figure 1. Explain the significance of the observer in the measurement of velocity.Apply principles of vector addition to determine relative velocity. ![]()
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