basic_engineering_mathematics0

206 Basic Engineering Mathematics
Assignment 12
This assignment covers the material in Chapters 25 and
26. The marks for each question are shown in brackets
at the end of each question.
4. A triangular plot of land ABC is shown in Fig. A12.1.
Solve the triangle and determine its area. (10)
15 m 71°
A
1. Plot a graph of y = 3x 2 + 5 from x = 1 to x = 4.
Estimate, correct to 2 decimal places, using 6 intervals,
the area enclosed by the curve, the ordinates x = 1 and
x = 4, and the x-axis by (a) the trapezoidal rule, (b) the
mid-ordinate rule, and (c) Simpson’s rule. (12)
Fig. A12.1
B
15.4 m
C
2. A circular cooling tower is 20 m high. The inside diameter
of the tower at different heights is given in the
following table:
Height (m) 0 5.0 10.0 15.0 20.0
Diameter (m) 16.0 13.3 10.7 8.6 8.0
Determine the area corresponding to each diameter
and hence estimate the capacity of the tower in cubic
metres. (7)
5. A car is travelling 20 m above sea level. It then travels
500 m up a steady slope of 17 ◦ . Determine, correct to
the nearest metre, how high the car is now above see
level. (3)
6. Figure A12.2 shows a roof truss PQR with rafter
PQ = 3 m. Calculate the length of (a) the roof rise PP ′ ,
(b) rafter PR, and (c) the roof span QR. Find also (d) the
cross-sectional area of the roof truss. (12)
3. A vehicle starts from rest and its velocity is measured
every second for 6 seconds, with the following results:
Time t (s) 0 1 2 3 4 5 6
Velocity v (m/s) 0 1.2 2.4 3.7 5.2 6.0 9.2
Using Simpson’s rule, calculate (a) the distance travelled
in 6 s (i.e. the area under the v/t graph) and (b) the
average speed over this period. (6)
P
3m
40° 32°
Q
P′
Fig. A12.2
R