1. P.4.3.1 2. P.4.3.2 3. P.4.3.3 Vraag 4 Vir die massa in P.4.3.3 by t = 3sek. bereken: (a) Die hoekspoed van die massa om die oorsprong. (b) Die krommingstraal van die boom. (c) Die koordinate van die krommingsmiddelpunt. Question 4 For the mass in P.4.3.3 at t = 3sec. calculate: (a) The angular velocity of the mass around the origin. (b) The radius of curvature of the trajectory. (c) The coordinates of the centre of curvature.

(d) Die hoekspoed om die krommingspunt.

(d) The angular velocity around the centre of curvature.

1

OPLOSSINGS VIR OEFENKLAS 4 SOLUTIONS TO TUTORIAL 4

P.4.3.1 vx = v0 cos θ, vy = v0 sin θ − gt x = v0 t cos θ 1 y = v0 t sin θ − gt2 2 (a) The projectile moves up when vy is positive and down when vy is negative. vy = v0 sin θ − gt = 0 when t = The projectile is at ground level when 2v0 sin θ 1 y = 0 = t v0 sin θ − gt ⇒ t = 0 or t = 2 g Thus for t ∈ 0, v0 sin θ the projectile is moving up and for t ∈ g projectile is moving down. at t = t0 = 0, vy = v0 sin θ at t = 2v0 sin θ 2v0 sin θ , vy = v0 sin θ − g g g = −v0 sin θ v0 sin θ 2v0 sin θ , g g

v0 sin θ = ttop g

the

The velocity in the y direction is of the same size as the initial velocity but in the opposite direction (down as opposed to upwards). (b) v = v0 cos θˆ + (v0 sin θ − gt) y ¯ x ˆ |¯| = v(t) = v = 2 2 v0 cos2 θ + v0 sin2 θ − 2v0 sin θgt + g 2 t2 2 v0 − 2gv0 t sin θ + g 2 t2

(c) When the projectile hits the ground, y = 0 thus t= The distance from the origin is x= 2 2v0 sin θ cos θ g

2v0 sin θ g

2

The maximum displacement is found when dx dθ dx dθ = 0, = = d2 x

...that I would like to be involved in is the AppliedMathematics discourse community. A lot of the time, people engulfed in the Applied Math discourse community are usually part of another discourse community. For example, Angela Gallegos, a math professor at LMU, got her PhD in Mathematics but also focuses on applying that to Biology. She is not only in the Applied Math discourse community, but in the Biology discourse...

...INTRODUCTION
Statistics and mathematics are everything to economics. infact statistics and Mathematics, the economic field wouldn't even exist.
Economist need statistics to represent data, to track and store information, to identify trends, to attribute value and mathematics to calculate those figures.The way to look at the relationship between statistics and economics is that economics is essentially the study of human decisions and trends, and...

...Mathematics Standard Level Maths SL workshop - InThinking Portfolio Task ~ Student Checklist
■ ■ ■ ■ ■ ■
■ ■
■ ■ ■
■
Does your portfolio report read like an article for a mathematical journal? Can your portfolio report be read without referring to the task questions? Does the introduction give a brief overview of the report and its purpose? Does the conclusion summarize the findings?
Has unnecessary repetition been avoided? Are graphs, tables and diagrams sufficiently...

...Luc Brubaker
Final Project
Rhetorical Arts
Writing in the Applied Math Discourse Community
A discourse community that I would like to be involved in is the AppliedMathematics discourse community. Although James Paul Gee claims that it is not that simple to join a discourse community, it is even more so in the appliedmathematics discourse community because of how broad it is. A lot of the time, people engulfed in the...

...Not my own work but it is fun to read.
_________________________________________
How is Statistics Different from Mathematics?
And Why Is the Distinction Important?
By
Isidoro P. David
Acronyms: CHED-Commission on Higher Education; NHERA-National Higher Education Research Agenda; HEI-Higher Education Institution; PSA- Philippine Statistical Association; SRTC-Statistical Research and Training Center; UPD-SS- University of the Philippines School of Statistics;...

...The importance of Mathematics
In such a modern and non-stop developing world nowadays, most people need mathematics as an important tool for their occupation, no matter what it is. Obviously, mathematics plays a vital role in daily use such as architecture, business, clerical work, etc... We even use math to balance our budget, pay bills, check our saving accounts, etc. Math is an important part of our civilization.
Most people using...

...Mathematical Application Projects for Mechanical Engineers Concept, Guidelines and Examples
Burkhard Alpers FH Aalen - University of Applied Sciences
balper@fh-aalen.de http://www.fbm.fh-aalen.de/
Abstract: In this article, we present the concept of mathematical application projects as a means to enhance the capabilities of engineering students to use mathematics for solving problems in larger projects as well as to communicate and present mathematical...

...Maths and other subjects relation
Mathematics and its importance
Mathematics is a fundamental part of human thought and logic, and integral to attempts at understanding the world and ourselves. Mathematics provides an effective way of building mental discipline and encourages logical reasoning and mental rigor. In addition, mathematical knowledge plays a crucial role in understanding the contents of other school subjects such as science, social...