2324-MM293 Level M Applied Math Final T2 Page 1 of 6

SABIS® FINAL APPLIED MATH

SAMPLE QUESTIONS
2324-MM293

1. Consider the two vectors r1= and r2= , and let R be the vector given by R = 2r1 - 3r2.
Fill in the blanks.
-11 + (_______)j
R= (_______)i 9

2. A vector is given by v = 12i + 5j.

v can be expressed as v = (r, θ), where r is its magnitude and θ is the counter-clockwise angle it
makes with the positive x-axis.
Fill in the blanks.
13
Given to the nearest integers, r = _________ 23
and θ = _________ o
.

3. A mass m1 = 3.0 kg moving at 4.0 m/s collides head-on with a mass m2 = 2.0 kg moving at 8.0
m/s in the opposite direction.
Fill in the blanks.
a. If the collision between the masses is perfectly inelastic, the velocity of mass m1 relative to
0 m/s.
mass m2 right after collision will be ______
b. If the collision between the masses is perfectly elastic, the mechanical energy of the system of
88 J.
masses after collision will be ________

4. An aluminum block of mass 10.0 kg rests on a rough plane inclined at θ = 30.0°. The box moves
at a constant velocity v along the inclined surface shown below. Take g = 10.0 m/s2.

Choose the correct answer.

The magnitude of the normal reaction on the box is ( 86.6 / 50 / 8.66 / 5.0 / 25.9 ) N.

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5. Consider the vectors a = –1 + 2j and b = 5i + 6j.

Fill in the blank.
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The scalar product of these two vectors is _________.

6. The diagram below shows a force-displacement graph describing a spring being stretched.

Fill in the blank.

3
The net work done on the spring is __________ J.

7. A particle of mass 3.0 kg, moving at 2.0 m/s, is subject to a force of 60 N acting parallel to its
displacement over 1.5 m.
Fill in the blank.
8
The final speed of the particle is __________ m/s.

8. Drag and drop to fill in the blanks.

mass sum force acceleration momentum rate of change zero

force acting upon a system is zero, the total ________________

If the net external ________ momentum of the
constant
system is ____________.

9. A particle is confined to move along a straight line.

The particle is initially at x = –5.0 m, moving away from the origin with an instantaneous speed of
2.0 m/s and a constant acceleration of magnitude 1.0 m/s2 .
Fill in the blank.
-6.5 m.
The position of the particle at t = 3.0 s is x = _________

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10. A javelin is thrown with an initial velocity of 20.0 m/s at an angle of 60.0° above the horizontal.
Take g = 10.0 m/s2 and neglect the size of the athlete and air resistance.

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The maximum height reached by the javelin is _________________ m.

11. A basketball is thrown with an initial velocity of 30.0 m/s at an angle of 45.0° above the horizontal.
Take g = 10 m/s2 and neglect the height of the athlete and air resistance.

90
The range of the projectile is R = _________________ m.

12. A 5.0 kg cart is being pulled by a rope, making an angle of 60o with the rough horizontal floor. The
tension in the rope is 30 N, resulting in a constant acceleration of 2.00 m/s2.

Fill in the blank.

Write the answer to the nearest integer.
5
The friction on the cart is ____________ N.

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13. An aircraft travelling at 123 km/hr must perform a circular curve of radius 400 m.
Use g = 10 m/s2.
Fill in the blank.
16 o.
The angle of banking of the aircraft, given to the nearest integer, is _________

14. A spring of constant 1200 N/m is stretched by 0.05 m.

Fill in the blank.
1.5 J.
The elastic potential energy stored in the spring is _________

15. Consider the diagram below.

A box of weight 20 N rests on a rough inclined plane that makes an angle of 37° with the
horizontal. Take g = 10 m/s2.

Fill in the blanks. Write the answers to the nearest integer.

12
a) The magnitude of friction on the box is __________ N.
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b) The magnitude of the normal reaction on the box is __________ N.

16. A radio controlled car moves along a circular track at a constant speed, making one complete
rotation every 8s.

0.25 π m/s.
The angular velocity of the car is _________

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17. A particle moves along the x-axis from point A ( x = –3 m ) straight to point B ( x = 9.25 m ) then
to point C ( x = 4 m ). The journey from A to C takes 3.5 seconds.
Fill in the blank.
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The average speed of the particle in the whole journey is ________ m/s.

18. A stationary rifle of mass 3.0 kg fires a bullet of mass 20 g with a speed of 180 m/s.
Fill in the blank. Write the answer to one decimal place.
1.2 m/s.
The rifle recoils with a speed of ________

19. Consider a body executes uniform circular motion.

What is the angle between the position vector and the velocity vector? Choose the correct answer.
( 0 / 60 / 45 / 90 / 180 )

20. Consider two point masses:

M1 = 200. g located at point ( 2.0 m ; 5.0 m )
M2 = 300. g located at point ( –10 m ; 7.0 m ).
Fill in the blank.
6.2 m).
-5.2 m; _______
The center of mass of this system is located at point ( _______

21. A force of 300. N is exerted for 0.40 s on a body.

Fill in the blank.
120 N.s.
The impulse imparted by this force is _______

22. Consider the function y = f(x) = (3x2 – 2x + 3). The derivative of y is.
[-A-]. x2 – x
[-B-]. 6x – 2
[-C-]. 3x – 2
[-D-]. 3x
[-E-]. 6x

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23. A man of mass 75 kg climbs 20 stairs each of height 0.150 in 5.00 s. Use g = 9.8 m/s2.
Fill in the blank.
441 W.
The average power developed by the man is ______

24. A motor cyclist moves along a circular track of radius 1000 m and constant speed of 20 m/s.
Choose the correct answer.
The magnitude of the centripetal acceleration of the particle is ( 0 m/s2 / 0.1 m/s2 / 0.2 m/s2 / 0.3 m/s2
/ 0.4 m/s2 ).

25. A parcel of 7 kg rests on a smooth horizontal surface. A force of 14 N is applied for 5.0 s.
Fill in the blank.
10 m/s.
The final speed of the parcel is _____

26. A sailing boat is acted upon by two forces, the wind force Fwind and water resistance Fres, as shown
in the diagram below.

When is the boat in translational equilibrium? Choose the correct answer.

( Fwind + Fres = 0 / Fwind × Fres = 0 / Fwind = 0 / Fres = 0 / Fdrag / Fres = 0 )

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