Short Answer

1. 108 cm, $\mathrm{\theta <!--\; \theta \; -->}={119.0}^{\circ <!--\; \circ \; -->}$
2. 108 cm, $\mathrm{\theta <!--\; \theta \; -->}={125.0}^{\circ <!--\; \circ \; -->}$
3. 206 cm, $\mathrm{\theta <!--\; \theta \; -->}={119.0}^{\circ <!--\; \circ \; -->}$
4. 206 cm, $\mathrm{\theta <!--\; \theta \; -->}={125.0}^{\circ <!--\; \circ \; -->}$

1. 108 cm, $\mathrm{\theta <!--\; \theta \; -->}={119.1}^{\circ <!--\; \circ \; -->}$
2. 108 cm, $\mathrm{\theta <!--\; \theta \; -->}={201.8}^{\circ <!--\; \circ \; -->}$
3. 232 cm, $\mathrm{\theta <!--\; \theta \; -->}={119.1}^{\circ <!--\; \circ \; -->}$
4. 232 cm, $\mathrm{\theta <!--\; \theta \; -->}={201.8}^{\circ <!--\; \circ \; -->}$

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?

1. Zero
2. Six
3. Eight
4. 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 39.5°. What is the magnitude of the net force exerted on the trolley?

1. 0.0 N
2. 79.6 N
3. 82.8 N
4. 88.0 N

True or False—A vector can form the shape of a right angle triangle with its x and y components.

1. True
2. False

True or False—All vectors have positive x and y components.

1. True
2. False

1. $R_x=\frac{A_x}{B_x}$
2. $R_x=\frac{B_x}{A_x}$
3. $R_x=A_x+B_x$
4. $R_x=A_x-<!--\; -\; -->B_x$

1. $R_y=\frac{A_y}{B_y}$
2. $R_y=\frac{B_y}{A_y}$
3. $R_y=A_y+B_y$
4. $R_y=A_y-<!--\; -\; -->B_y$

When a three dimensional vector is used in the study of atmospheric sciences, what is z?

1. Altitude
2. Heat
3. Temperature
4. Wind speed

Which method is not an application of vector calculus?

1. To find the rate of change in atmospheric temperature
2. To study changes in wind speed and direction
3. To predict changes in atmospheric pressure
4. To measure changes in average rainfall

1. $\stackrel{\to <!--\; \to \; -->}{v}=\stackrel{\to <!--\; \to \; -->}{a}t$
2. $\stackrel{\to <!--\; \to \; -->}{v}=\stackrel{\to <!--\; \to \; -->}{v_0}+\stackrel{\to <!--\; \to \; -->}{a}t$
3. $\stackrel{\to <!--\; \to \; -->}{v}+\stackrel{\to <!--\; \to \; -->}{v_0}=\stackrel{\to <!--\; \to \; -->}{a}t$
4. $\stackrel{\to <!--\; \to \; -->}{v_0}+\stackrel{\to <!--\; \to \; -->}{v}+\stackrel{\to <!--\; \to \; -->}{a}t$

In the equation for the maximum height of a projectile, what does $v_{0y}$ stand for? $$h=\frac{v_{0y}{}^2}{2g}$$

1. Initial velocity in the x direction
2. Initial velocity in the y direction
3. Final velocity in the x direction
4. Final velocity in the y direction

True or False—Range is defined as the maximum vertical distance travelled by a projectile.

1. True
2. False

1. $0^{\circ <!--\; \circ \; -->}$ or ${30}^{\circ <!--\; \circ \; -->}$
2. $0^{\circ <!--\; \circ \; -->}$ or ${45}^{\circ <!--\; \circ \; -->}$
3. ${90}^{\circ <!--\; \circ \; -->}$ or $0^{\circ <!--\; \circ \; -->}$
4. ${90}^{\circ <!--\; \circ \; -->}$ or ${45}^{\circ <!--\; \circ \; -->}$

1. $\text{N}$
2. $\text{m/s}$
3. ${\text{m/s}}^2$
4. unitless

1. It increases with the increase in the relative motion.
2. It decreases with the increase in the relative motion.
3. It remains constant and is independent of the relative motion.

1. When the magnitude of the component of the weight along the slope is equal to the magnitude of the frictional force.
2. When the magnitude of the component of the weight along the slope is greater than the magnitude of the frictional force.
3. When the magnitude of the component of the weight perpendicular to the slope is less than the magnitude of the frictional force.
4. When the magnitude of the component of the weight perpendicular to the slope is equal to the magnitude of the frictional force.

1. $0^{\circ <!--\; \circ \; -->}$
2. ${30}^{\circ <!--\; \circ \; -->}$
3. ${60}^{\circ <!--\; \circ \; -->}$
4. ${90}^{\circ <!--\; \circ \; -->}$

What is the term used for changes in shape due to the application of force?

1. Amplitude
2. Deformation
3. Displacement
4. Restoring force

What is the restoring force?

1. The normal force on the surface of an object
2. The weight of a mass attached to an object
3. Force which is applied to deform an object from its original shape
4. Force which brings an object back to its equilibrium position

For a given oscillator, what are the factors that affect its period and frequency?

1. Mass only
2. Force constant only
3. Applied force and mass
4. Mass and force constant

For an object in simple harmonic motion, when does the maximum speed occur?

1. At the extreme positions
2. At the equilibrium position
3. At the moment when the applied force is removed
4. Midway between the extreme and equilibrium positions

What is the equilibrium position of a pendulum?

1. When the tension in the string is zero
2. When the pendulum is hanging straight down
3. When the tension in the string is maximum
4. When the weight of the mass attached is minimum

If a pendulum is displaced by an angle θ, what is the net restoring force it experiences?

1. mgsinθ
2. mgcosθ
3. –mgsinθ
4. –mgcosθ