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What I Need to Know
This module was designed and written with you in mind. It is here to help you master the Motion in 2-3 Dimensions. The scope of this module permits it to be used in many different learning situations. The language used recognizes the diverse vocabulary level of students. The lessons are arranged to follow the standard sequence of the course. But the order in which you read them can be changed to correspond with the textbook you are now using.
The module has one lesson, namely: Relative motion Position, distance, displacement, speed, average velocity, instantaneous velocity, average acceleration, and instantaneous acceleration in 2- dimensions
After going through this module, you are expected to:
- describe motion using the concept of relative velocities in 1D and 2D; and
- extend the definition of position, velocity and acceleration of 2D and 3D using vector representation
What I Know
Directions: Choose the letter of the best answer. Write the chosen letter in your notebook.
- Which of the following is the motion of objects moving in two dimensions under the influence of gravity? a. Horizontal velocity c. Projectile Motion b. Mechanics d. Vertical Velocity
- Which of the following does not exhibit parabolic motion? a. A baseball thrown to home plate b. A frog jumping from land into water c. A flat piece of paper released from a window d. A baseball thrown to a hoop
- What is the path of projectile (in the absence of friction)? a. A wavy line c. A parabola b. A hyperbola d. none of the above
- When an object is moving with a uniform circular motion, the centripetal acceleration of the object a. is circular b. is constant c. is directed toward the center of motion is constant d. is perpendicular to the plane of motion
- What term describes a change in the speed of an object in circular motion? a. centrifugal force c. centripetal force b. centripetal acceleration d. tangential speed
Numbers 6-
In a parking lot a rabbit across on which a set of coordinate axes has been formulated. Given is the rabbit’s position in meters as a function of time in seconds.
x = -0.31 t^2 + 7.2 t + 28 y = 0.22 t^2 -0.91t + 30
- What is the rabbit’s position vector in unit vector notation? a. 20 m, 50 m c. 26 m, 57 m
b. 26 m, -57 m d. 57 m, 26 m
- What is the magnitude of angle notation?
a. 30^0 b. 35^0 c. 40^0 d. 41^0
- What is the rabbit’s velocity v at time t = 15 s?
a. 3.1 m/s b. 3.22 m/s c. 3.3 m/s d. 3.4 m/s
- What is the angle of velocity?
a. -100^0 b. -130^0 c. 100^0 d. 130^0
- What is the acceleration a at time t= 15s?
a. 0.70 m/s^2 b. 0.75 m/s^2 c. 0.76 m/s^2 d. 0.80 m/s^2
- A ball rolls off the edge of a table. The horizontal component of the ball's velocity remains constant during its entire trajectory because
a. the ball is not acted upon by any force. b. the net force acting on the ball is zero.
c. the ball is not acted upon by a force in the horizontal direction.
d. None of the other choices is correct.
- A monkey is sitting at the top of a tree 20 m high from the ground level. A person standing on the ground wants to feed the monkey. He uses a bow and arrow to launch the food to the monkey. If the person knows that the monkey is going to drop from the tree at the same instant that the person launches the food, how should the person aim the arrow containing the food?
a. He should aim it at the monkey.
b. He should aim it below the monkey. c. He should aim it above the monkey.
d. None of the other choices is correct.
- An athlete throws a ball with a velocity of 40 m/s at an angle of 20e above the horizontal. Which of the following statements is true in this case?
a. The vertical component of the velocity remains constant. b. The horizontal component of the velocity changes.
c. The vertical component of the velocity changes sign after the ball attains its maximum height.
d. The horizontal component of the velocity changes sign after the ball attains its maximum height.
- For general projectile motion, which statement is true when the projectile is at the initial and final points of the parabolic path?
What is It
Position
Position vector r
specifies position of an object in three dimensions and in a given coordinate systems it it is described by three numbers,
r
= (x, y, z) = x i ˆ^ + y ˆ j^ + z k ˆ
One can imagine an arrow connecting the origin with position of object to describe r
. If the object is in motion, then the position changes with time the position vector becomes a function (actually three functions) of time
r
(t)=(x(t), y(t), z(t)) = x(t) i ˆ^ + y(t) j ˆ^ + z(t) k ˆ
These three functions do depend on the coordinate system, but as was already noted the physically measurable quantities should not depend on this choice.
Velocity
Similarly to 1D case in 3D we can define average velocity vector as
v
avg ≡ ∆^ r
∆t = r
(t 2 ) − r
(t 1 ) t 2 − t 1
(where ∆⃗ r is now the displacement vector) and instantaneous velocity vector
v
(t) ≡ lim ∆t→0 v
avg = lim ∆t→0 ∆^ r
∆t = d r
(t) dt
Acceleration
Similarly to 1D case in 3D we can define average acceleration vector as a
avg ≡ ∆^ v
∆t = v
(t 2 ) − v
(t 1 ) t 2 − t 1
What’s More
Game: FACT OR BLUFF
Identify the statement if it is FACT or BLUFF
__________ 1. Displacement of a particle is the change of position vector during a certain time.
__________ 2. Average velocity of a particle moves through a distance in t.
__________ 3. The direction of the instantaneous velocity of a particle is always tangent to the particle’s position.
__________ 4. The trajectory of a simple projectile is hyperbola.
__________ 5. Uniform circular motion can be described as the motion of an object in a circle at a constant speed.
__________ 6. Centrifugal force is the force which keeps the body move along the axis of rotation and this force is acting always toward the center.
__________ 7. Displacement is the distance covered by an object or body with specified direction.
__________ 8. Acceleration the change of velocity per unit time.
__________ 9. Deceleration is negative acceleration.
__________ 10. Speed and velocity had the same set of units like m/s, km/h, cm/s, mi/h they are only differ in terms of direction.
__________ 11. Distance and displacement had the same units as m, km, mi they are only differ in terms of direction.
__________ 12. Range is the total distance covered by an object or body in projectile motion.
__________ 13. Instantaneous velocity is the velocity of an object or body at a particular time.
__________ 14. Instantaneous acceleration is the acceleration at a particular time or instant.
__________ 15. Motion in 1 dimension considered the horizontal and vertical components of motion.
What I Can Do
- Cite 5 examples of motion in 2 to 3 dimensions.
- Illustrate your 5 examples the position, displacement and acceleration in vector notation.
Assessment
Directions: Choose the letter of the best answer. Write the chosen letter in your notebook.
- Which of the following is the motion of objects moving in two dimensions under the influence of gravity?
a. Horizontal velocity c. Projectile Motion b. Mechanics d. Vertical Velocity
- Which of the following does not exhibit parabolic motion? a. A baseball thrown to home plate
b. A frog jumping from land into water
c. A flat piece of paper released from a window d. A baseball thrown to a hoop
- What is the path of projectile (in the absence of friction)?
a. A wavy line c. A parabola b. A hyperbola d. none of the above
- An athlete throws a ball with a velocity of 40 m/s at an angle of 20e above the horizontal. Which of the following statements is true in this case?
a. The vertical component of the velocity remains constant.
b. The horizontal component of the velocity changes. c. The vertical component of the velocity changes sign after the ball attains its maximum height.
d. The horizontal component of the velocity changes sign after the ball attains its maximum height.
- For general projectile motion, which statement is true when the projectile is at the initial and final points of the parabolic path?
a. The magnitude of the x and y components of its velocity are same at both points.
b. The magnitude of its x component of velocity at the initial point is smaller than its magnitude of the y component of velocity at the final point. c. The magnitude of its x component of velocity at the initial point is bigger than its magnitude of the y component of velocity at the final point.
d. The velocity components are zero at both points.
- If the initial speed of a projectile is doubled.
a. Its range will double. b. Its range will be decreased by a factor of two.
c. Its range will quadruple.
d. Its range will decrease by a factor of four.
Additional Activities
Make a crossword puzzle for those terms utilized on motion in 2 to 3 dimensions. Illustrate the characteristics of the term/s on the across and down part.
DOWN ACROSS
What I Need to Know
This module was designed and written with you in mind. It is here to help you master
the accuracy and precision. The scope of this module permits it to be used in many different learning situations. The language used recognizes the diverse vocabulary level
of students. The lessons are arranged to follow the standard sequence of the course.
But the order in which you read them can be changed to correspond with the textbook
you are now using.
The module has one lesson, namely:
Components of Projectile Motion
After going through this module, you are expected to:
- Define projectile motion.
- Describe and draw the motion of object
- Explain the independence of projectile motion in vertical and horizontal components.
What I Know
Read each problem or situations carefully. Choose the letter of the correct answer and
write it in your notebook.
- What is a projectile? a. a motion b. a motion with angle c. object d. path
- Which of the following motion is experienced by a projectile thrown or fired along the surface of the earth? a. horizontal motion b. projectile motion c. random motion d. vertical motion
- What is the vector representation of the projectile motion? a. circular arrow b. downward arrow c. vertical arrow d. Upward arrow
- What do you call the motion of object moving in two dimensions under the influenced of gravity? a. circular motion b. horizontal motion
