INSTRUCTIONS: Answer question ONE and any other TWO questions

Some useful constants;
Acceleration due to gravity, g= 9.8 ms-2
1 mile = 1609 m = 1.609 km 1 ft = 0.3048 m = 30.48 cm
1 m = 39.37 in. = 3.281 ft 1 in. = 0.0254 m = 2.54 cm
1 lb = 0.465 kg 1 oz = 28.35 g 1 slug = 14.59 kg
1 day = 24 hours = 24 * 60 minutes = 24 * 60 * 60 seconds
Question One
a) (i) What is the difference between fundamental quantities and derived quantities? [3 Marks]
(ii) Convert the speed limit of 80 km/hr to m/s [2 Marks]
(iii) A car is traveling at a speed of 38.0 m/s. Is the driver exceeding the speed limit stated in (ii)?
[2 Marks]
b) What are the fundamental units of the following?
i) Mass [1 Mark]
ii) Length [1 Mark]
iii) Time [1 Mark]
c) Determine the dimensions of the following quantities:
(i) volume [1 Mark]
(ii) acceleration [1 Mark]
(iii)density [1 Mark]
(iv)force [1 Mark]
(v) charge [1 Mark]
d) A 16kg block rests on a horizontal surface. A force of 5N is required to cause the block to break
away and start moving, a force of 3N is sufficient to keep the block sliding at a constant speed once
it is set in motion. Calculate the kinetic and static coefficients of friction. [3 Marks]
e) A force has x, y components of 3 and 4 respectively.
i) Express the force as a vector in rectangular coordinates. [2 Marks]
ii) Determine the magnitude of the force. [2 Marks]
f) What are the differences in the arrangement of molecules in a solid, liquid and a gas? [3 Marks]
g) With the aid of clearly labeled sketches describe the terms specular and diffuse reflection[3 Marks]
h) The wavelength of red light in air is 633nm but 474nm in the liquid inside the eyeball.
i) Calculate the index of refraction of the liquid in the eyeball. [2 Marks]
ii) Determine the speed and frequency of the light in the substance. [3 Marks]
Question Two
a) A lift starts at ground level and accelerates as 1.2 m/s2
for 5s. It then moves with uniform speed for
10s and finally stops at the top floor of a building with retardation (deceleration) of 2.0 m/s2
(i) Draw the speed time graph of the motion [6 Marks]
(ii) What is the height of the building? [4 Marks]
b) (i) Briefly define freefall. [3 Marks]
(ii) A worker drops a hammer from the top of a 60m high building. If the speed of sound in air
is 340 m/s, how long does the worker have to shout down to warn colleagues (if his warning is
to reach them before the hammer!) Neglect air resistance. [7 Marks]
Question Three
a) A football kicker can give the ball an initial speed of 25 m/s.
What are the least and greatest elevation angles at which he can kick the ball to score a field goal
from a point 50. m in front of goalposts whose horizontal bar is 3.44 m above the ground ? [4 Marks]
b) A car is driven east for a distance of 50 km, then north for 30 km, and then in a direction 30o
east of
north for 10 km.
i) Draw a vector diagram for the motion of the car. [4 Marks]
ii) Determine the magnitude and direction of the final displacement of the car from its starting
point. [6 Marks]
c) A roller coaster cart of mass m= 300 kg starts at rest at point , whose height off the ground is h1=
25m , and a little while later reaches point , whose height off the ground is h2=7m . What is the
potential energy of the cart relative to the ground at point ? What is the speed of the cart at point
, neglecting the effect of friction? [4 Marks]

Question Four
a) A car of mass 1000 kg traveling at 30m/s has its speed reduced to 10m/s by a constant breaking
force over a distance of 75m.
(i) The cars initial kinetic energy [5 Marks]
(ii) The final kinetic energy [5 Marks]
(iii)The breaking force [5 Marks]
b) A 0.075 kg arrow is fired horizontally. The bow string exerts an average force of 65 N on the arrow
over a distance of 0.90m. What speed does the arrow have upon leaving the bow? [5 Marks]
Question Five
a) (i) A wave has a wavelength of 15 cm and has a frequency of 10 waves/second. Determine the
speed of the wave? [3 Marks]
(ii) The speed of a wave on a rope is 50cm/s and it’s wavelength is 10cm. What is it’s frequency?
[3 Marks]
(iii) A wave is traveling with a velocity of 125m/s and has a frequency of 20 waves/second. What
is the length of the wave? [3 Marks]
b) The speed of sound in air is a bit over 300 m/s, and the ratio of the frequency of the light wave to
that of the sound wave is about 1000000. Suppose we make a sound wave and a light wave that
both have a wavelength of 3 meters.
i. Determine the speed of light in air. [3 Marks]
ii. Determine the frequencies of light and sound waves [3 Marks]
iii.Write down the equation of a general harmonic wave. [2 Marks]
iv. Show how your equation can be modified to indicate the direction of the wave
motion. [3 Marks]

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