Short Answer
5.1 Vector Addition and Subtraction: Graphical Methods

108 cm, \theta = 119.0^\circ

108 cm, \theta = 125.0^\circ

206 cm, \theta = 119.0^\circ

206 cm, \theta = 125.0^\circ

108 cm, \theta = 119.1^\circ

108 cm, \theta = 201.8^\circ

232 cm, \theta = 119.1^\circ

232 cm, \theta = 201.8^\circ
Consider six vectors of 2 cm each, joined from head to tail making a hexagon. What would be the magnitude of the addition of these vectors?
 Zero
 Six
 Eight
 Twelve
Two people pull on ropes tied to a trolley, each applying 44 N of force. The angle the ropes form with each other is 39.5Â°. What is the magnitude of the net force exerted on the trolley?
 0.0 N
 79.6 N
 82.8 N
 88.0 N
5.2 Vector Addition and Subtraction: Analytical Methods
True or Falseâ€”A vector can form the shape of a right angle triangle with its x and y components.
 True
 False
True or Falseâ€”All vectors have positive x and y components.
 True
 False

R_x = \frac{A_x}{B_x}

R_x = \frac{B_x}{A_x}

R_x = A_x + B_x

R_x = A_x  B_x

R_y = \frac{A_y}{B_y}

R_y = \frac{B_y}{A_y}

R_y = A_y + B_y

R_y = A_y  B_y
When a three dimensional vector is used in the study of atmospheric sciences, what is z?
 Altitude
 Heat
 Temperature
 Wind speed
Which method is not an application of vector calculus?
 To find the rate of change in atmospheric temperature
 To study changes in wind speed and direction
 To predict changes in atmospheric pressure
 To measure changes in average rainfall
5.3 Projectile Motion

v = at

v = v_0 + at

v + v_0 = at

v_0 + v + at
In the equation for the maximum height of a projectile, what does ${v}_{0y}$ stand for? $$h=\frac{{v}_{0y}{}^{2}}{2g}$$
 Initial velocity in the x direction
 Initial velocity in the y direction
 Final velocity in the x direction
 Final velocity in the y direction
True or Falseâ€”Range is defined as the maximum vertical distance travelled by a projectile.
 True
 False

0^\circ\! or 30^\circ

0^\circ\! or 45^\circ

90^\circ\! or 0^\circ

90^\circ\! or 45^\circ
5.4 Inclined Planes

\text{N}

\text{m/s}

\text{m/s}^2

unitless

It increases with the increase in the relative motion.

It decreases with the increase in the relative motion.

It remains constant and is independent of the relative motion.

When the magnitude of the component of the weight along the slope is equal to the magnitude of the frictional force.

When the magnitude of the component of the weight along the slope is greater than the magnitude of the frictional force.

When the magnitude of the component of the weight perpendicular to the slope is less than the magnitude of the frictional force.

When the magnitude of the component of the weight perpendicular to the slope is equal to the magnitude of the frictional force.

0^\circ

30^\circ

60^\circ

90^\circ
5.5 Simple Harmonic Motion
What is the term used for changes in shape due to the application of force?
 Amplitude
 Deformation
 Displacement
 Restoring force
What is the restoring force?
 The normal force on the surface of an object
 The weight of a mass attached to an object
 Force which is applied to deform an object from its original shape
 Force which brings an object back to its equilibrium position
For a given oscillator, what are the factors that affect its period and frequency?
 Mass only
 Force constant only
 Applied force and mass
 Mass and force constant
For an object in simple harmonic motion, when does the maximum speed occur?
 At the extreme positions
 At the equilibrium position
 At the moment when the applied force is removed
 Midway between the extreme and equilibrium positions
What is the equilibrium position of a pendulum?
 When the tension in the string is zero
 When the pendulum is hanging straight down
 When the tension in the string is maximum
 When the weight of the mass attached is minimum
If a pendulum is displaced by an angle Î¸, what is the net restoring force it experiences?
 mgsinÎ¸
 mgcosÎ¸
 â€“mgsinÎ¸
 â€“mgcosÎ¸