# Question-   LO1: Identify the relevance of mathematical methods to a variety of conceptualised engineering examples.  Solution-

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a- The speed of sound in a gas might plausibly depend on the pressure , the density , and the volume of the gas. Use dimensional analysis to determine the exponents , and in the formula. where is a dimensionless constant. Incidentally, the units of pressure are kilograms per meter per second squared.

b- Force of viscosity F acting on a spherical body moving through a fluid depends upon its velocity (v), radius (r) and co-efficient of viscosity ‘η’ of the fluid. Using method of dimensions obtain an expression for ‘F’.

c- An arithmetic progression has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference. Find also the sum of the geometric series 8 − 4 + 2 − 1 + . . . where there are 5 terms in the series.

d- An airplane is approaching point A along a straight line and at a constant altitude h. At 10:00 am, the angle of elevation of the airplane is 20o and at 10:01 it is 60o . What is the altitude h of the airplane if the speed of the airplane is constant and equal to 600 miles/hour? (round answer to 2 decimal places)                    Lot: Id the relevance of mathematical methods to a of conceptualised ‘engineering examples. P a The speed of sound v in a gas might plausibly depend on the pressure, the Pp density’ , and the volume V of the gas. Use dimensional analysis to determine the y = pVE exponents z, and z in the formula. = CP*P”V*; where Cis a dimensionless constant. Incidentally, the units of pressure are kilograms per meter per second squared. 'b- Force of viscosity F acting on a spherical body moving through a fluid depends upon its velocity (v), radius (r) and co-efficient of viscosity ‘n! of the fluid. Using method of dimensions obtain an expression for ‘F’ - An arithmetic progression has 3 as its first term. Also, the sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference. Find also the sum of the geometric series 8-4 +2- 1+... where there are 5 terms in the series. d- An airplane is approaching point A along a straight line and at a constant altitude h. At 10:00 am, the angle of elevation of the airplane is 20° and at 10:01 it is 60°. What is the altitude h of the airplane if the speed of the airplane is constant and equal to 600 miles/hour? (round answer to 2 decimal places). e- A radioactive substance has a half-life of one week. In other words, at the end of every ‘week the level of radioactivity is half of its value at the beginning of the week. The initial level of radioactivity is 20 counts per second.

7 Draw the graph of the amount of radioactivity against time in weeks. 2- Find the formula that gives the radioactivity in terms of time. 3+ Find the radioactivity left after three weeks. The following data shows the number of people (in thousands) who own an apple cell phone device in Canada. Year [2000 [2002 [2004 [2006 008 Number off 225 ‘375 je23 1037 1725 Icell-Phone Owners \thousands) 1- Determine an exponential equation which fits this data 2. Ifthe increase in sales continues to increase at this rate, use the model to predict how ‘many people will own a cell phone in 2026. 3+ Determine the average rate of change between the year 2006 and 2010. 4 Determine the instantaneous rate of change in 2006.

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