Higher Engineering Mathematics, Sixth Edition

Revision Test 4

This Revision Test covers the material contained in Chapters 11 to 13.The marks for each question are shown in
brackets at the end of each question.

1. A 2.0m long ladder is placed against a perpen-
   dicular pylon with its foot 52cm 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 10cm towards the pylon how far
   does the top of the ladder rise? (7)


2. Evaluate correct to 4 significant figures:
   (a) cos124◦ 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 30m 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 .5cosec 31◦ 17 ′−cot(− 12 ◦)

3sec79◦ 41 ′

(5)

6. A man leaves a point walking at 6.5km/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
   directionE 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 80km apart
   after 5hours. (8)


7. A crank mechanism shown in Fig. RT4.1 com-
   prises armOP, of length 0.90m, which rotates
   anti-clockwise about the fixed point O,and
   connecting rodPQof length 4.20m. EndQmoves
   horizontally in a straight lineOR.
   (a) If∠PORis initially zero, how far does end
   Qtravel in^14 revolution.

O Q

P

R

Figure RT4.1

(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, 3rad) (6)


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


11. 140mm of a belt drive is in contact with a pul-
    ley of diameter 180mm 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 RT4.2 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 portion,
    and (c) the area of the unshaded area. (11)

h

12 cm

608

12 cm

Figure RT4.2

13. Determine, (a) the co-ordinates of the centre of
    the circle, and (b) the radius, given the equation

x^2 +y^2 − 2 x+ 6 y+ 6 =0(7)