IB Mathematics HL IA (19/20): Investigation into the time taken for a parachutist to reach the terminal velocity

본 문서는 2016년 IB 수학 HL IA이며, 연구 주제는 Investigation into the time taken for a parachutist to reach the terminal velocity 입니다. 제가 고안해낸 연구 주제를 토대로 IA를 작성하였으며 누구의 도움 없이 학생이던 시절 당시에 19/20 이라는 점수를 받았기 때문에 현재 타인의 도움없이 혼자서 IA를 쓰고 있는 학생에게 도움이 될 것입니다.

[본문내용]

Introduction

Differential Equation refers to all the equation that relates a function with its derivatives. [1] Different forms of differential equations are found in various different areas, including engineering, physics, economics, biology, etc. For example, the motion of pendulum can be expressed in the form of differential equation, 2 2 + sin = 0, [2] where both the function of θ and the second derivative of θ are both in a single equation.

Rationale

From when I was in elementary school, I read a book that was about elementary physics knowledge. Then, I saw that when a parachute is falling, the time the parachute reaches the terminal velocity is actually dependent on lots of factors. Then, I always wondered what factors would be determining the time it takes for a parachutist to reach the terminal velocity. After, I read a book, which said the parachutist’s velocity and the acceleration when falling can be expressed in a form of differential equation. Therefore, I chose to explore the topic of parachute motion. As I have wondered it, I will be investigating some key factors that would determine the time it takes for the parachutist to reach the terminal velocity, and to do that, I will be researching on the first order differential equations and their solutions, as I was truly interested on differential equations when I was searching their definitions and examples, and the expression of the motion of the parachutist is also a first order differential equation…

• 총 페이지수: 13 pages
• 과목: Math
• 주제: Investigation into the time taken for a parachutist to reach the terminal velocity
• The file is in PDF format.