9 Module 9 - Q1 - GENERAL PHYSICS 1
9 Module 9 - Q1 - GENERAL PHYSICS 1
9 Module 9 - Q1 - GENERAL PHYSICS 1
1
General Physics 1 – Grade 12 STEM
Republic Act 8293, section 176 states that: No copyright shall subsist
in any work of the Government of the Philippines. However, prior approval of
the government agency or office wherein the work is created shall be
necessary for exploitation of such work for profit. Such agency or office may,
among other things, impose as a condition the payment of royalties.
2
MELC Most Essential Learning Competency
3
MODULE 1: Relative Velocity
In your Junior High School years, you were taught that force can make things
in motion. Right? But how can you say really that a certain object is in motion? Do all
moving objects can be considered in motion?
Let us find out the answers to those questions in this module. Moreover, this
module will help us recognize that motion is relative by understanding the reference
frame.
LEARNING TARGETS:
4
Oops! Just a minute. Take the
pre-test first.
PRE - TEST
1. A car has a velocity of 5 m/s due North. A bus has a velocity of 2 m/s due to
South. What is the setup of the velocity of the car relative to the bus?
A. 𝑣𝐶𝐵 = 𝑣𝐶𝐺 + 𝑣𝐵𝐺
c= car B. 𝑣𝐶𝐵 = 𝑣𝐺𝐶 + 𝑣𝐶𝐵
b= bus C. 𝑣𝐵𝐶 = 𝑣𝐶𝐵 + 𝑣𝐵𝐺
g= ground D. 𝑣𝐵𝐶 = 𝑣𝐵𝐺 + 𝑣𝐺𝐶
A. 3. 3 m/s
B. 6.0 m/s
C. 5.0 m/s
D. 8.3 m/s
A. 40 mph
B. 50 mph
C. 10 mph
D. 30 mph
5
LEARNING ACTIVI TIES
“I refer on You”
• Analyze the given situation below and answer the guide questions that follow.
GUIDE QUESTIONS:
2. How does the starting position affect Luigi’s way in finding the library?
______________________________________________________________
______________________________________________________________
3. From the above situation, how will you define reference frame?
______________________________________________________________
______________________________________________________________
6
“Looks can be Deceiving”
• Analyze the given situation below and give your insight right after.
Two students followed the path shown below in going to their classroom.
Student A followed the straight path (red line) while Student B followed the
curved path (green line). Mario and Luigi argued which of the two students
covered the greater displacement.
Library Classroom
https://bit.ly/2DgiY36
Mario
https://bit.ly/2PloSm7
Luigi https://bit.ly/2DwM8
Toad
From the three characters above, which statement or idea do you agree?
Why?
I agree with…
______________________________________________________________
______________________________________________________________
______________________________________________________________
7
ACTIVITY 1: Velocity: Below the City
• Study the mathematical equation below to infer the idea of relative velocity.
HINT: 𝑣𝐴𝐵 = 𝑣𝐴 - 𝑣𝐵 𝑣𝐶𝐵 = 𝑣𝐶 - 𝑣𝐵
Each velocity is labelled by 𝑣𝐵𝐴 = 𝑣𝐵 - 𝑣𝐴 𝑣𝐶𝐷 = 𝑣𝐶 - 𝑣𝐷
two subscripts: the first
𝑣𝐵𝐶 = 𝑣𝐵 - 𝑣𝐶 𝑣𝐷𝐶 = 𝑣𝐷 - 𝑣𝐶
refers to the object, the
second to the reference
frame in which it has this
Therefore,
velocity.. 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 𝑣𝑜𝑏𝑗𝑒𝑐𝑡− 𝑣𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑓𝑟𝑎𝑚𝑒
Based on the above mathematical equation, how will you define relative
velocity?
______________________________________________________________
______________________________________________________________
Train A with person A inside moves at 50 miles per hour with respect to
the ground. Train B with person B inside moves at 60 miles per hour in the
same direction. What is the relative velocity of train A with respect to B and
relative velocity of train B with respect to train A?
Given: Find:
VAB = VA - VB VBA = VB – VA
VAB = 50 mph -60 mph VBA = 60 mph -50 mph
VAB = - 10 mph VBA = 10 mph
GUIDE QUESTIONS:
1. How will you describe the motion of train A and B relative to the ground?
___________________________________________________________
2. How will you describe the motion of train A relative to train B?
__________________________________________________
3. How will you describe the motion of train B relative to A?
_______________________________________________
8
Remember: When velocities are along the same line (one dimension), simple addition (taking
account the direction of the object) or subtraction is sufficient to obtain relative velocity. But if
they are not along the same line (two-dimension), we must make use of vector addition
emphasizing the reference frame. Making a vector diagram will make it easier to calculate
relative velocity in two-dimension.
2. A boat heads North at 3.5 m/s directly across a 200 m wide river flowing
east at 1.7 m/s.
a. What is the velocity of the boat relative to the shore?
________________________________________________________
________________________________________________________
b. How long will it take to cross the river?
________________________________________________________
________________________________________________________
c. How far downstream will the boat be when it crosses the river?
________________________________________________________
________________________________________________________
9
The concept of relative motion in one and two-dimension depends
on our understanding of the motion itself and the reference frame.
As you can see, in the elicit part of this module, you were given a
situational activity where you can learn that the observer’s point of
view affects the way they perceived things. The same thing happens
when you are sitting in a train at a station and you see another train moving. You will
feel like you are moving though you are stationary at the platform. To you, sitting on
the stationary train (A), or to the person on the platform, the moving train (B) appears
to be travelling at a velocity 𝑣 away. However, to the person on the moving train, the
platform and the train sitting stationary both appear to be moving in the opposite
direction with the same speed, or to put it another way, with the opposite velocity.
So, reference frame plays a crucial role to better understand relative velocity.
On the engage activity, you were able to realize the idea of motion in one and
two dimension. The motion of an object along a straight path/line or along either x or
y axis only is known as motion in one dimension. When the object moves along x
and y axis at the same time, it is now considered as motion in two dimension.
Activity 1
With the given mathematical equation above, you have learned that relative
velocity is the vector difference between the velocities of two bodies. Each velocity
is labelled by two subscripts: the first refers to the object, the second to the reference
frame in which it has this velocity. Moreover, in understanding relative velocity of an
object if the reference frame is not stated, it means that it will always be with respect
to something that is stationary.
Activity 2
Activity 3
When the velocities are along the same line (one dimension), simple addition
(taking account of the direction of the object) or subtraction is sufficient to obtain
relative velocity. But if they are not along the same line (two-dimension), we must
make use of vector addition emphasizing the reference frame. Making a vector
diagram will make it easier to calculate relative velocity in two-dimension.
10
In activity 3, problem no. 1 is an example of relative motion in one dimension,
so Anna’s velocity relative to the ground is zero since she is just standing still at the
airport. The velocity of Dodong relative to Carla is 1.0 m/s and can be obtained by
subtracting Carla’s velocity relative to Anna from Dodong’s velocity relative to Anna.
Since it is stated that Dodong is walking at his normal walking speed on the platform
(P), his normal walking speed is just VDP. We can calculate this because we know
how fast both the platform and Dodong are moving away from Anna. The velocity of
Dodong relative to the platform is 1.0 m/s likewise the velocity of Carla relative to
Bert is also 1.0 m/s. Problem no. 2 is an example of relative motion in two dimension
wherein the boat travels North while the river flows East. Though the boat is heading
North, it will move Eastward since the river is flowing East. Hence, its motion is along
both x and y. For problems involving relative motion in two dimension, you will use
Pythagorean Theorem to get the relative velocity and SOH-CAH-TOA for the
direction.
• Study the picture below to answer the guide questions that follows
1. Find the velocity of the crab relative to the ship, if the ship is heading east at
100 km/h while the crab is moving at 3m/s North.
11
2. Green fish is moving 2m/s East while pink fish is due West at 4m/s. What is
the relative velocity of the fishes to each other?
3. Describe the relative velocity of the star fish with respect to the light house if it
is stationary in its current position?
4. How will you explain the importance of relative velocity in describing the
motion of the object?
1. A boat heads North at 2.8 m/s across a river flowing East at 1.3 m/s. (a) What
is the velocity of the boat relative to the shore? (b)What is the new position of
the boat relative to its starting point after 5 seconds?
12
• Create a scenario similar to the one above where you can show the relative
velocity of object in motion in
A. one dimension
B. two dimension
VOCABULARY LIST
Distance- is a total path length traversed by an object moving from one location to
another.
Displacement- is a vector quantity defined as the distance between the initial point
and final point of an object.
Relative velocity- is the vector difference between the velocities of two bodies.
Vector Diagram- are diagrams that depict the direction and relative magnitude of a
vector quantity by a vector arrow. This can be used to describe the velocity of a
moving object during its motion.
13
ANSWER KEY
P r e - T e s t
1. A
2. B
3. A
4. A
5. D
14
VDC = 3.0 m/s – 2.0 m/s
VDC= 1.0 m/s
c) Since it is stated that Dodong is walking at his normal walking speed on
the platform (P). His normal walking speed is just V DP. We can calculate
this because we know how fast both the platform and Dodong are moving
away from Anna. The velocity of Dodong relative to the platform is:
VDP= VDA- VPA
VDP= 3.0 m/s – 2.0 m/s
VDP = 1.0 m/s
Therefore, Dodong’s normal walking speed is 1.0 m/s
d) The velocity of Carla relative to Bert is:
VCB= VCA- VBA
VCB= 2.0 m/s – 1.0 m/s
VDP = 1.0 m/s
Note: In here, we will make use of a vector The above figure shows the vector diagram when
equation using the Pythagorean Theorem the boat heads north and the river flowing east.
a2+b2= c2 since a right triangle is formed.
15
b) The river is 200 m wide and the boat is heading North at 3.5 m/s. Let 𝑑𝑦 = 200 m
𝑑
and 𝑣𝑦 = 3.5 m/s (since it is moving along y axis). Using the speed formula v= 𝑡 ,
let us find t. 𝑑
𝑡=
𝑣
200 𝑚
𝑡=
3.5 𝑚/𝑠
𝑡 = 57. 14 s
c) The river is moving at 1.7 m/s East so the distance downstream is basically the
horizontal displacement equated as 𝑑𝑥= 𝑣 ∙ t. Substitute the value,
𝑑𝑥= 𝑣 ∙ t
𝑚
𝑑𝑥= (1.7 ) ∙ (57. 14 𝑠)
𝑠
𝑑𝑥= = 97.14 𝑚
100 𝑘𝑚 100 𝑚 1ℎ
1. × × = 27. 78 𝑚/𝑠 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
tanӨ = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
ℎ 1 𝑘𝑚 3600 𝑠
2. 6 m/s West
16
1. a) 𝑣𝐵𝑆
2
= 𝑣𝐵𝑊 + 𝑣𝑊𝑆
2 2
𝑣𝐵𝑆 = 𝑣𝐵𝑊 + 𝑣𝑊𝑆
2 2
𝑣𝐵𝑆 = √𝑣𝐵𝑊 + 𝑣𝑊𝑆
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
tanӨ = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝑣𝑊𝑆
tanӨ= 𝑣𝐵𝑆
1.3 𝑚/𝑠
tanӨ= 2.8 𝑚/𝑠
1.3 𝑚/𝑠
Ө= tan -1 (2.8 𝑚/𝑠)
65. 1°
Ө= 24.90 °
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
tanӨ = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝑣𝑊𝑆
tanӨ= Therefore, the new position of the boat is 15. 45 m at an
𝑣𝐵𝑆
angle of 24. 90° E of N.
6.5 𝑚/𝑠
tanӨ= 14 𝑚/𝑠
2. a) The river is moving at 0.7 m/s West so the distance downstream is basically
the horizontal displacement equated as 𝑑𝑥= 𝑣 ∙ t. Substitute the value,
𝑑𝑥= 𝑣 ∙ t
𝑚
𝑑𝑥= (0.7 ) ∙ (66. 67 𝑠)
𝑠
𝑑𝑥= = 46.67 𝑚
17
b) The river is 80 m wide and the swimmer is heading North at 1.2 m/s. Let 𝑑𝑦 = 80
𝑑
m and 𝑣𝑦 = 1.2 m/s. Using the speed formula v= 𝑡 , let us find t.
𝑑
𝑡=
𝑣
80 𝑚
𝑡=
1.2 𝑚/𝑠
𝑡 = 66. 67 s
3. Let us represent the velocity of the motorcycle as 𝑣𝑀 and the velocity of the
car as 𝑣𝐶 .
Now, the velocity of the motorcycle relative to the point of view of a passenger
is given as 𝑣𝑀𝐶 = 𝑣𝑀 - 𝑣𝐶
Substituting the values in the above equation, we get
𝑣𝑀𝐶 = 120 km/h – 90 km/h
𝑣𝑀𝐶 = 30 km/h
Therefore, the velocity of the motorcycle relative to the passenger of the car is
30 km/h
REFERENCES
• Physics-IntroductionToMotion-Relative Velocity.
https://byjus.com/physics/relative-velocity/
• https://quizizz.com/admin/quiz/5d95fdf6a3ca4b001af98b09/relative-
velocity
• https://www.youtube.com/watch?v=PyPxHimIr-0
• https://www.youtube.com/watch?v=8-mzp1lQo7E
18