MAT560 - Muhammad ALIF BIN Sidek (2021130911) PDF

Preview

Summary

FACULTY OF COMPUTER SCIENCE AND MATHEMATICSTITLE:PROJECTILE MOTION OF SOFTBALLERASSESSMENT 1: INDIVIDUAL ASSIGNMENTMAT 560 VECTOR CALCULUSCS2485DBY:MUHAMMAD ALIF BIN SIDEK(2021130911)MAY 2, 2022Table of ContentsContent Page1 Introduction 1. Motion in Space 1. Projectile Motion232 Case study 2 Situat...

Description

FACULTY OF COMPUTER SCIENCE AND MATHEMATICS

TITLE: PROJECTILE MOTION OF SOFTBALLER

ASSESSMENT 1: INDIVIDUAL ASSIGNMENT MAT 560 VECTOR CALCULUS CS2485D

BY: MUHAMMAD ALIF BIN SIDEK (2021130911)

MAY 2, 2022

Table of Contents Content

Page

1.0 Introduction 1.1. Motion in Space

2 3

1.2. Projectile Motion

2.0 Case study 2.1 Situation

4

2.2 Problem Statement

4

3.0 Mathematical work

5

Reference

6

1

1

1.0 INTRODUCTION 1.1. Motion in Space Motion consists of three characteristics, which is velocity, speed, and acceleration. (() ,  ( ), and ( (�) are the velocity, speed, and acceleration of a particle, respectively. All the following information may be applied to either plane or space curves.

In addition, for your knowledge, velocity is a vector while speed is a scalar.

Symbol

Formula

( (�)

�

′

�

′′

‖� ′ (�)‖

Definition

(((())+ += (()) () +()

Position vector function of a particle in motion at time t



Velocity of the particle at time t

�

�

Acceleration of the particle at time t

� �

Speed of the particle at time t

� Table 1.1.1

Let �:

be a path of a particle in motion. Formula

Definition

� Arc length of � Displacement =

The distance travelled by the particle along C The displacement of the particle on [

� Table 1.1.2

1.2. Projectile Motion Projectile motion is an object moving with an initial velocity but with no forces acting on it other than gravity. An object can travel both horizontally and vertically at the same time.

When both velocity and acceleration are known, vector integrals can be used to recover them. If the force acting on the particle is known, Newton's Second Law of Motion,  =  (�), can be used to calculate the acceleration. Term and Formula 

Definition The initial velocity

0

�

Angle of elevation of the projectile

�0

The initial position of object from the ground

�0

The initial height of the object

((( ) = ( 0 s co ) s)

Horizontal distance of object projected Height of the object form the ground

1 ((( ) = ( 0n n si ))n) −

2

+ℎ 2

ⅆ �max =

Maximum height of the object projected =0

ⅆ

3

(�)

2.0 CASE STUDY 2.1 Situation In my case study, I have chosen Cricket sports as an application of projectile motion. In this sports, the player who batting the ball is called The Batsman. This thought came to me suddenly as I was looking at a player. At an initial speed of 80 m/sec, a batsman hits a ball 30 degrees above the horizontal. The batsman stands at a height of 190cm. I am curious about the projectile's position vector at time t. Aside from that, by looking at the ball, I would like to know what the ball's maximum height could reach. Therefore, what is the initial speed of the ball if the batsman hits it 35 degrees above the horizontal and it takes 10 seconds to hit the ground?

2.2 Problem Statement i.

The position vector of projectile at time t.

ii.

The maximum height the ball can reach.

iii.

The initial speed of the ball when the batter hits a ball at a 35° above the horizontal for 10 seconds to hit the ground.

4

3.0 MATHEMATICAL WORK

i.

The initial speed, �ₒ=80m/s ��2+h]

� (t) = (vₒ cos a) ti + [(vₒ sin a) t -

(t) = (80 cos 30) ti + [(80 sin 30) t - 8 9.82+1.9] (t) = 69.2820ti + [40t – 4.9�2+1.9]

ii.

Maximum height is reached when the � component of (′ (�) is zero. (′ (�) = 69.2820i + [40 8 −9.8] Let 8 40−9.8 = 0 → � = 40/9.8 = 4.082 Maximum height, � (4.082): = 40(4.082) −4.9 (4.082)2 +1.9 = 83.5327

iii.

((( ) = ( 0 n n sin ) −1/2 2 +ℎ (() = 

0

ⅈ35) (10) – 1/2(9.8) (10)

0 8 = 5.7358 0 − 490 +1.9 0 8 = 5.7358 0 −491.9 8 5.7358 0 = 491.9  0=  0= / 85.7596 /

5

2

+1.9

Reference

Moebs , W.(2016).University Physic Volume 1.OpenStax. https://opentextbc.ca/universityphysicsv1openstax/chapter/3-4-motion-with-constantacceleration/

Projectile Motion Overview. (2016). Lumenlearning.com https://courses.lumenlearning.com/physics/chapter/3-4-projectilemotion/#:~:text=Projectile%20motion%20is%20the%20motion,path%20is%20called%20its %20trajectory.

6...