### 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?

*mg*sin*Î¸**mg*cos*Î¸*- â€“
*mg*sin*Î¸* - â€“
*mg*cos*Î¸*