1. a.) 0.236 m/s, b.) 0.150 m/s (upwards), c.) 0.472 m/s (to the right)

2. These are Proofs and have no numerical answers. HINT: they start with the lecture given definitions of acceration, <v>, and displacement.

3. 20.4 m

4.

b) T= 4.00 s

a)

5. Graph

6. a) a = 8.66 m/s^{2 }, b) N = 74.1 N

7. a.) P/5m, b.) P/5, c.) 2P/5

8. a) Graph b) Description – no numbers

9. Graph

10. a) downward, b) Upward from center of Earth

11. a.) Diagram, as per lecture b.) 5.00 m/s^{2}, c.) 11.2 m/s^{2}

UNITS AND DIMENSIONS. VECTORS AND SCALARS.

1. A child drops a marble into a deep pool. After falling some distance, it attains a constant velocity, v_{t}. At this velocity, the resistive force on the marble upwards is equal to the net downwards force on the marble. The terminal velocity v_{t}is given by the equation:

where r is the radius of the marble, ρ is the density of the marble and η is the viscosity of water. Find a unit for η in terms of base units. (4 marks)

2. The time period of a simple pendulum of mass m and spring constant k is given by the equations:

Show that this expression is consistent with k being measured in Nm^{-1}. (4 marks)

3. a. Explain what it means to say that a physical equation is homogeneous.

b. Show that the equation below is homogeneous:

(4 marks)

4. Explain the difference between a vector and a scalar. What is meant by the magnitude of a vector? Use a diagram to illustrate your answer. (4 marks)

5. Which of the following physical parameters are vectors: capacitance, displacement, electric field, mass, momentum, frequency, kinetic energy, weight? (4 marks)

6. Vector is twice as long as vector , and the angle between both vectors is 45˚. Draw two vector diagrams to clearly show i) and ii) . (4 marks)

7. The vector is added to the vector . What is the magnitude of the resultant vector? (4 marks)

8. A car has a velocity of 18.0 m s^{-1} due north. At a junction, its turns 90.0º to the left and its new velocity is 14.0 m s^{-1}.

a. Draw a vector diagram to show the initial and final velocities and the change in velocity

b. Calculate the change in speed

c. Calculate the change in velocity (6 marks)

9. A river flows from west to east at 3.00 km h^{-1}. Two athletic teenagers, Harry and Jack, leave a point O on the river’s south bank simultaneously. Harry canoes such that his actual motion is due north at 6.00 km h^{-1}. Jack runs east, along the river at 10.0 km h^{-1}.

Use clearly labelled vector diagrams to find the speed, in km h^{-1}, and direction of Harry

a. relative to Jack

b. relative to the water (6 marks)

10. Two coplanar forces A and B act at a point O, as shown in the figure below (in Newtons). Calculate the component of the resultant force

a. along OX

b. along OY

c. the magnitude and direction of the resultant force.

(6 marks)

11. What is the resultant force for the vectors shown?