Higher Engineering Mathematics

Assign-04-H8152.tex 23/6/2006 15: 7 Page 146

Geometry and trigonometry

Assignment 4

This assignment covers the material contained

in Chapters 12 to 14.

The marks for each question are shown in

brackets at the end of each question.

1. A 2.0 m long ladder is placed against a perpen-
   dicular pylon with its foot 52 cm from the pylon.
   (a) Find how far up the pylon (correct to the near-
   est mm) the ladder reaches. (b) If the foot of the
   ladder is moved 10 cm towards the pylon how
   far does the top of the ladder rise?
   (7)


2. Evaluate correct to 4 significant figures:
   (a) cos 124◦ 13 ′ (b) cot 72. 68 ◦ (4)


3. From a point on horizontal ground a surveyor
   measures the angle of elevation of a church spire
   as 15◦. He moves 30 m nearer to the church and
   measures the angle of elevation as 20◦. Calculate
   the height of the spire. (9)


4. If secant θ= 2 .4613 determine the acute
   angleθ (4)


5. Evaluate, correct to 3 significant figures:
   3 .5 cosec 31◦ 17 ′−cot (− 12 ◦)
   3 sec 79◦ 41 ′

(5)

6. A man leaves a point walking at 6.5 km/h in
   a direction E 20◦N (i.e. a bearing of 70◦). A
   cyclist leaves the same point at the same time
   in a direction E 40◦S (i.e. a bearing of 130◦)
   travelling at a constant speed. Find the average
   speed of the cyclist if the walker and cyclist are
   80 km apart after 5 hours. (8)


7. A crank mechanism shown in Fig. A4.1 com-
   prises armOP, of length 0.90 m, which rotates
   anti-clockwise about the fixed pointO, and con-
   necting rodPQof length 4.20 m. EndQmoves
   horizontally in a straight lineOR.

P

O Q R

Figure A4.1

(a) If∠PORis initially zero, how far does end

Qtravel in^14 revolution

(b) If ∠POR is initially 40◦ find the angle

between the connecting rod and the horizon-

tal and the lengthOQ

(c) Find the distanceQmoves (correct to the

nearest cm) when∠PORchanges from 40◦

to 140◦ (16)

8. Change the following Cartesian co-ordinates
   into polar co-ordinates, correct to 2 decimal
   places, in both degrees and in radians:
   (a) (−2.3, 5.4) (b) (7.6,−9.2) (10)


9. Change the following polar co-ordinates into
   Cartesian co-ordinates, correct to 3 decimal
   places: (a) (6.5, 132◦) (b) (3, 3 rad) (6)


10. (a) Convert 2.154 radians into degrees and
    minutes.
    (b) Change 71◦ 17 ′into radians (4)


11. 140 mm of a belt drive is in contact with a pul-
    ley of diameter 180 mm which is turning at 300
    revolutions per minute. Determine (a) the angle
    of lap, (b) the angular velocity of the pulley, and
    (c) the linear velocity of the belt assuming that
    no slipping occurs. (9)


12. Figure A4.2 shows a cross-section through a
    circular water container where the shaded area
    represents the water in the container. Determine:
    (a) the depth,h, (b) the area of the shaded