TUTORIAL 1
MEASUREMENT
1. Change 360 km hour-1 into SI unit.
2. If M = (3i + 5j), N = (i + 3j), k =constant,show that k(M + N) = kM + Kn
3. If F = 2i +3j and X = 4i +2j are the force acting on an object and it displacement
4.
5.
6.
respectively,find:
a) The magnitude of F and X,
b) The magnitude of the work done
c) The angle between F and X
Given OA = 2i + j – 3k, and OB = 3i + 2j + 2k. Find the magnitude of the cross
product.
Given vector A and B in terms of unit vectors as : A= 2i –j –k ,B= 3i -5j +2k. Calculate
the angle between the two vectors.
Given that A and B in terms of unit vector as A = 3i + 5j -2k, B = -3j +6k, determine C
such that 2A + 7B + 4C= 0
Find the angle between vectors 2i + j - k and i - k.
7.
1
8. The displacement of an object is expressed by 𝑠 = 𝑢𝑡 + 2 𝑎𝑡 2 , where 𝑢 =
(22.52 ± 0.01)𝑚𝑠 −1 , 𝑡 = (4.5 ± 0.01)𝑠 𝑎𝑛𝑑 𝑎 = (5.6 ± 0.1)𝑚𝑠 −2 calculate the
displacement and its uncertainty.
9. Let: a = 2î + 5ĵ and b = 5î - 3ĵ hence find
a) a + b
b) 2a – 3b
c) |2a|
10. The horizontal and the vertical components of the velocity of a ball after being kicked
are 3.0ms-1 and 4.0ms-1 respectively. Determine the magnitude and direction of the
velocity of the ball.
11. A beetle crawls on a wall. Its location is determined by the coordinates x = 60mm
and y = 80mm with respect to the origin. Determine the magnitude and direction of
the position vector r.
12. An aeroplane travel 4.50×102 km due east and then travels an unknown distance due
north. Finally it returns to its starting point by travelling a distance of 525 km. How
far did the airplane travel in the notherly direction?
13. If a car is travelling at a speed of 28.0m/s, is the driver exceeding the speed limit of
55.0mi/h?
14. Determine the resultant vector. Given that F1 = 10N, F2 = 5N, Ѳ1 = 25o and Ѳ2 = 30o
15. Three displacement vectors is shown in FIGURE 1
B
A
450
450C
i.
ii.
resultant displacement in unit vector
magnitude and direction of the resultant displacement
16. Fighter jet starting from airbase A flies 300km east, 350km at 30.0º west of north,
and then 150km north to arrive finally at airbase B
a) The next day, another fighter jet flies directly from A to B in a straight line. In what
direction should the pilot travel in this direct flight?
b) How far will the pilot travel in this direct flight?
17. A particle undergoes three consecutive displacements:
d1=(15i+30j+12k)cm
d2=(23i-14j-5k)cm
d3=(-13i+15j)cm
Find the components of the resultant displacement and its magnitude.
18. Given 2 vectors:
A= (3i+2j-4k)
B= (-5i+8j-2k)
Calculate
a) the value of A•B
b) the angle θ between 2 vectors
19. Two forces F1 and F2 of magnitude 15.0 N and 10.0 N respectively ae applied at
point O. Both forces are inclined at an angle of 50 to the x- axis.
Calculate
a) The x and y components of each of the forces
b) The vector sum of the x and y component of these forces
c) The resultant forces
20. .An object of weight 49N is suspended by two strings which are at 30° and 70° to the
vertical as shown below. What are the tensions in the strings?
T1
70°
30°
T2
w