1a) A surveyor uses a steel measuring tape that is exactly 50.000 m long at a temperature of 20C. The markings on the tape are calibrated for this temperature. Given that the coefficient of linear expansion for steel is .1:

ii. What is the length of the tape when the temperature is 35C?

iii. When it is 35C, the surveyor uses the tape to measure a distance. The value that she reads off the tape is 35.794 m. What is the actual distance?

b) A gold purchasing company bought a bar of gold with a volume of 1.84 cubic inches. What is the volume in cubic centimeters? In cubic meters? [Note: 1 inch=2.54cm]

c) A small piece of ice is placed on a table. Eventually, the water converts from the ice at

1=32.00 to body temperature, 2=98.60. Express these temperature in both Celsius and Kelvins degrees, and find the .=.2.1 in both cases.

QUESTIONS 2

Figure 1

a) What are the x and y-components of vector .in Figure 1(a) if the magnitude of the vector .is 3.00m, and the angle, .=45.

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b) What are the x and y-components of vector .in Figure 1(b) if the magnitude of the vector .is 4.50m, and the angle, .=37.

c) In a middle of a road your car breaks down and you begin to push it to the nearest repair shop. How does the force you exert on the car compare to the force the car exerts on you when the car is starting to move? How do these forces compare when you are pushing the car along at a constant speed?

QUESTIONS 3

a) Obtain the resultant of the following three displacement vectors:

. : 72.4m, 32.0 east of north

.: 57.3m, 36.0 South of west

. : 17.8m, due south

b) A boy hits two identical balls with the same initial speed and from the same initial height but at different initial angles. Explain why both balls have the same speed at any height h if air resistance can be neglected.

c) A worker applies a constant horizontal force with a magnitude of 20 N to a box with a mass of 40 kg resting on a level floor with negligible friction. What is the acceleration of the box?

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QUESTION 4

a) Suppose that the x-velocity, Vx, of a car at any time t is given by the equation

..=..+.......

ii) Find the change in x-velocity of the car in the time interval, .1=1.0. to .2=3.0..

iiii) Find the average x-acceleration in this time interval.

iiiiii) Assuming the mass of the car is 1200kg, find the average force in this time interval [ [10 Marks]

ivb) A submarine periscope uses two totally reflecting 454590 prisms with total internal reflection on the sides adjacent to the 45 angles. Explain why the periscope will no longer work if it springs a leak and the bottom prism is covered with water.

c) The energy, E, of an object with mass m is given by .=..2, where .=2.99792458 . 108m/s. Calculate, correct to 3 significant figures, the energy E given that .=9.11 . 1031kg. Hint: 1.=1...2/.2.

QUESTION 5

a) A police car's siren emits a sinusoidal wave with frequency = 300 Hz. The speed of sound is 340 m/s and the air is still.

ii. Find the wavelength of the waves if the siren is at rest.

iiii. Find the wavelengths of the waves in front of and behind the siren if it is moving at 30 m/s.

. [8 marks]

b) A driver moving towards east via a small town accelerates at a constant 4.0./.2 after he leaves the city limits. At t=0, he is 5.0m east at 15./..

i) Find his position and velocity at t=2.0s.

c) Where is he when his velocity is 25m/s

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d) In a scene from a sci-fi movie, a rocket is moving in the vacuum of outer space, far from any star or planet, when its engine dies. As a result, the spaceship slows down and stops. Does this contradict with Newton's first law of motion? Explain.