Component, Unit, and R Position Vectors

How do you calculate the Y component of a velocity vector given its magnitude and angle above the horizontal?

• Divide the magnitude by the cosine of the angle

• Multiply the magnitude by the cosine of the angle

• Divide the magnitude by the sine of the angle

• Multiply the magnitude by the sine of the angle

What is the mistake in saying that the sum of the X and Y components of a vector equals the original vector without considering direction?

• The direction of each component must be considered

• The components should be divided, not added

• The original vector is always larger than the sum of its components

• The components should be multiplied, not added

Why are unit vectors used to describe vectors?

• They provide a clear representation of direction and magnitude

• They simplify calculations by avoiding trigonometric functions

• They eliminate the need for vector diagrams

• They are only used in two-dimensional problems

In the vector addition example, what is the resultant vector when adding A = 2.0i + 2.0j, B = 1.0i - 3.0j, and C = 4.0i + 4.0j?

• 6.0i + 3.0j

• 7.0i + 2.0j

• 7.0i + 3.0j

• 6.0i + 2.0j

What is the first step in calculating the distance between two positions using unit vectors?

• Subtract the two position vectors

• Find the magnitude of each position vector

• Determine the components of each position vector

• Add the two position vectors

When given an angle east of north, which trigonometric function is used to find the X component of a vector?

• Cosine

• Cotangent

• Sine

• Tangent

What is the magnitude of the displacement vector if the change in position is given by 5.39i + 9.07j meters?

• 12.0 meters

• 9.5 meters

• 11.0 meters

• 10.6 meters

What does the R position vector represent in three-dimensional space?

• The speed of an object

• The location of an object

• The acceleration of an object

• The force acting on an object

What is the derivative of the position vector with respect to time?

• Average velocity

• Displacement

• Instantaneous velocity

• Acceleration

How can unit vectors help in understanding motion in three dimensions?

• They are only applicable in two-dimensional motion

• They allow simultaneous analysis of motion in all three dimensions

• They simplify calculations by reducing dimensions

• They eliminate the need for velocity calculations