This document is an assignment from a General Physics 101 course. It contains 6 multi-part physics problems involving vector addition and subtraction, finding magnitudes and directions of vectors, and using trigonometric functions to solve problems graphically and analytically. The instructor is Dr. Said Moh'd Azar.
International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
B.Sc (Pass) Nautical & Engineering Model Question 2 Mathematics Second Paper
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International Journal of Engineering Inventions (IJEI) provides a multidisciplinary passage for researchers, managers, professionals, practitioners and students around the globe to publish high quality, peer-reviewed articles on all theoretical and empirical aspects of Engineering and Science.
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
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This comprehensive document is a curated collection of meticulously crafted mathematics questions designed specifically for CBSE board exams. Covering a wide range of topics, the question bank aims to provide students with diverse and challenging problems, ensuring thorough preparation and a solid understanding of the curriculum. Ideal for self-assessment and exam practice, this resource serves as a valuable tool for students aspiring to excel in their CBSE mathematics examinations.
x
y
2.5 3.0 3.5
-1.0 6 7 8
1.0 0 1 2
3.0 -6 -5 -4
MATH 223
FINAL EXAM REVIEW PACKET ANSWERS
(Fall 2012)
1. (a) increasing (b) decreasing
2. (a) 2 2( 3) 25y z− + = This is a cylinder parallel to the x-axis with radius 5.
(b) 3x = , 3x = − . These are vertical planes parallel to the yz-plane.
(c) 2 2 2z x y= + . This is a cone (one opening up and one opening down) centered on the z-axis.
3. There are many possible answers.
(a) 0x = produces the curve 23y z= − .
(b) 1y = produces the curves 23 cosz x= − and 23 cosz x= − − .
(c)
2
x
π
= produces the curves 3z = and 3z = − .
4. (a) (b) (i) 1 (ii) Increase (iii) Decrease
5. (a) Paraboloids centered on the x-axis, opening up in the positive x direction. 2 2x y z c= + +
(b) Spheres centered at the origin with radius 1 ln c− for 0 c e< ≤ . 2 2 2 1 lnx y z c+ + = −
6. (a) 6 am 11:30 am
(b) Temperature as a function of time at a depth of 20 cm.
(c) Temperature as a function of depth at noon.
7. ( , ) 2 3 2z f x y x y= = − −
8. (a) II, III, IV, VI (b) I (c) I, III, VI (d) VI (e) I, V
9. (a)
12
4 12
5
z x y= − + (b) There are many possible answers.
12
4
5
i j k+ −
(c)
3 569
2
10. (a) iii, vii (b) iv (c) viii (d) ii (e) v, vi (f) i, ix
11. There are many possible answers.
(a) ( )5 4 3
26
i j k− +
or ( )5 4 3
26
i j k− − +
(b) 2 3i j− +
(c)
4
cos
442
θ = , 1.38θ ≈ radians (d) ( )4 4 3
26
i j k− +
(e) 4 11 17i j k− − −
12. (a)
3
5
a = − (b)
1
3
a = (c) 2( 1) ( 2) 3( 3) 0x y z− − + + − = (d)
1 2 , 2 , 3 3x t y t z t= + = − − = +
13. 6 39i
or 6 39i−
14. (a)
( )
2
23 2 2
3 2
3 1
z x y x
x x y x y
∂
= −
∂ + + +
(b)
( )4
10 4 3
5
H
H T
f
H
+ +
=
−
(c)
2
2 2
1 1z
x y y x
∂
= − −
∂ ∂
15. (a) 2 2 24 ( 1) 3 ( 2) 2z e x e y e= − + − + (b) 4( 3) 8( 3) 6( 6) 0x y z− + − + − =
16. (a)
2sin(2 ) cos(2 )
5 5
v v
ds dv d
α α
α= +
(b) The distance s decreases if the angle α increases and the initial speed v remains constant.
(c) 0.0886α∆ ≈ − . The angle decreases by about 0.089 radians.
17. (a) The water is getting shallower.
4
( 1, 2)
17
uh − = −
(b) There are many possible answers. 3i j+
(c) 72 ft/min
18. (a)
( )
2 2 2
22 2 22
2 2
1 1 11
yz xyz z yz
grad i j k
x x xx
= − + + + + + +
(b) ( ) ( ) ( )( )2 2 2 2curl x y z i y z j xz k i zj yk+ + − + + = + −
(c) ( ) ( ) ( )( )2 3 3cos sec 2 cos sin sec tan 3z zdiv x i x y j e k x x x y y e+ + = − + +
(d)
37
3
(e) ( , , ) sin zg x y z xy e c= + +
19. ( , ) 4 3vG a b = −
20. (a) positive (b) negative (c) negative (d) negative (e) positive (f) zero
21. (a)
(.
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Assignment 3-ch#2
1. Al-Farabi College
Name: …………………
General Physics 101 PHYS
Assignment III
Instructor: Dr. Said Moh’d Azar
Ch#2
1- Figure 2.18 shows a collection of vectors that can be combined in various ways. For
example, A+C=B. Find (a) E+C; (b) A+F; (c) A+D; (d) E+A; (e) E+2A; (f) A-B; (g)
B-A; (h) C-A.
2- In figure below, for what value of θ will C=A+B have (a) a maximum magnitude,
and (b) a minimum magnitude? (c) Find C when θ = 90°.
B=12
θ
A=5
2. 3- A vector has an x component of -10 and a y component of +3. (a) Draw a set of x-y
axes and show the vector. (b) Calculate the magnitude and direction of the vector.
4-
= 3 ̂ + 2 ̂,
= 4 ̂ − ̂. Find the magnitude of (a) A+B; (b) A-B; (c) 2B.
5-
= 2 ̂ + 4 ̂, Find the magnitude and direction of (a) A; (b) –A.
6- If θ=72° in figure below, find (a) the direction and magnitude of C=A+B by
constructing a drawing using a ruler and protractor; (b) the direction and magnitude
of C using the component method.
B=12
θ
A=5