Exam 3: Vectors and Coordinate Systems

In the figure,the magnitude of vector is 18.0 units,and the magnitude of vector is 12.0 units.What vector must be added to the vectors and so that the resultant of these three vectors points in the -x direction and has a magnitude of 7.50 units? Use vector components to find your answer,and express vector by giving its magnitude and the angle it makes with the +x-axis taking counterclockwise to be positive.

An apple falls from an apple tree growing on a 20° slope.The apple hits the ground with an impact velocity of 16.2 m/s straight downward.What is the component of the apple's impact velocity parallel to the surface of the slope?

The components of vector are = +2.2 and = -6.9 ,and the components of vector are given are = -6.1 and = -2.2.What is the magnitude of the vector - ?

Vector has a magnitude of 5.5 cm and points along the x-axis.Vector has a magnitude of 7.5 cm and points at +30° above the negative x-axis. (a)Determine the x and y components of Vector . (b)Determine the x and y components of Vector (c)Determine x and y components of the sum of these two vectors. (d)Determine the magnitude and direction of the sum of these two vectors.

You walk to the north,then turn 60° to your right and walk another How far are you from where you originally started?

Vectors and are shown in the figure.Vector is given by = - .The magnitude of vector is 16.0 units,and the magnitude of vector is 7.00 units.What is the magnitude of vector ?

A helicopter is flying horizontally with a speed of 444 m/s over a hill that slopes upward with a 2% grade (that is,the "rise" is 2% of the "run").What is the component of the helicopter's velocity perpendicular to the sloping surface of the hill?

Vectors and are shown in the figure.Vector is given by = - .The magnitude of vector is 16.0 units,and the magnitude of vector is 7.00 units.What is the angle of vector ,measured counterclockwise from the +x-axis?

Vector = -3.00 + 3.00 and vector = 3.00 + 4.00 .What is vector = + ?

An airplane undergoes the following displacements: First,it flies 66 km in a direction 30° east of north.Next,it flies 49 km due south.Finally,it flies 100 km 30° north of west.Using vector components,determine how far the airplane ends up from its starting point.

A teacher sends her students on a treasure hunt.She gives the following instructions: 1.Walk 300 m north 2.Walk 400 m northwest 3.Walk 700 m east-southeast and the treasure is buried there. As all the other students walk off following the instructions,Jane physics student quickly adds the displacements and walks in a straight line to find the treasure.How far and in what direction does Jane need to walk?

If - = 0,then the vectors and have equal magnitudes and are directed in the opposite directions from each other.

As shown in the figure,three force vectors act on an object.The magnitudes of the forces as shown in the figure are = 80.0 N, = 60.0 N,and = 40.0 N,where N is the standard SI unit of force.The resultant force acting on the object is given by