Exam 3: Vectors and Coordinate Systems

Vector has a magnitude of 75.0 cm and points at 30° above the positive x-axis. Vector has a magnitude of 25.0 cm and points along the negative x-axis. Vector has a magnitude of 40.0 cm and points at 45° below the negative x-axis. (a) Determine the x and y components of Vector . (b) Determine the x and y components of Vector . (c) Determine the x and y components of Vector . (d) Determine x and y components of the sum of these three vectors. (e) Determine the magnitude and direction of the sum of these three vectors.

If the magnitude of vector is less than the magnitude of vector , then the x component of is less than the x component of .

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?

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?

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

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?

Vector has a magnitude 5.00 and points in a direction 40.0° clockwise from the negative y axis. What are the x and y components of vector .

If all the components of a vector are equal to 1, then that vector is a unit 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.

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

What is the magnitude of + + , where = 1.00 + 4.00 - 1.00 , = 3.00 - 1.00 - 4.00 and = -1.00 + 1.00 ?

You walk 53 m to the north, then turn 60° to your right and walk another Determine the direction of your displacement vector. Express your answer as an angle relative to east.