Kinematics Part 2: Vertical Motion

Professor Dave Explains
30 Jan 201707:07
EducationalLearning
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TLDRIn this educational video, Professor Dave delves into vertical motion, emphasizing the constant acceleration due to Earth's gravity at -9.8 m/sΒ². He explains how this value affects the position and velocity of objects in free fall or thrown upwards, using examples of a rock dropped from a cliff and another thrown upwards. Through equations, he illustrates how to calculate the time and velocity of these objects, highlighting the importance of sign conventions in vertical motion analysis. The video aims to enhance understanding of kinematic equations and their application to vertical motion scenarios.

Takeaways
  • πŸ“Œ Vertical motion is similar to horizontal motion, but with a constant acceleration due to Earth's gravity (-9.8 m/sΒ²).
  • πŸ“Œ In vertical motion, the direction down is considered negative, while the positive direction is typically up.
  • πŸ“Œ Objects in free fall on Earth experience a uniform acceleration of -9.8 m/sΒ² regardless of their initial velocity.
  • πŸ“Œ The time it takes for an object to fall can be calculated using the position equation, with initial velocity set to zero.
  • πŸ“Œ The final velocity of a falling object can be determined using the velocity equation, accounting for the negative acceleration.
  • πŸ“Œ When an object is thrown upwards, its initial velocity decreases due to the acceleration of gravity, until it becomes zero and then turns into a negative acceleration as it falls back down.
  • πŸ“Œ The total time for an object thrown upwards andε›žθ½ takes longer than a freely falling object due to its initial upward motion.
  • πŸ“Œ The quadratic equation is used to solve for the time of flight when an object is thrown upwards, as the displacement and initial velocity are both non-zero.
  • πŸ“Œ The final velocity of an object thrown upwards and falling back down is greater than that of an object dropped, due to the additional height reached during its upward trajectory.
  • πŸ“Œ Understanding vertical motion is crucial for comprehending the principles of physics, and the same kinematic equations apply with the constant acceleration due to gravity.
  • πŸ“Œ The video provides a comprehensive tutorial on vertical motion, emphasizing the importance of sign conventions and the application of kinematic equations.
Q & A

  • What are the three key parameters discussed in the context of vertical motion?

    -The three key parameters discussed in the context of vertical motion are position, velocity, and acceleration.

  • What is the acceleration due to Earth's gravity, and how does it differ from horizontal motion?

    -The acceleration due to Earth's gravity is a constant -9.8 meters per second squared. It differs from horizontal motion in that it is always directed downwards, whereas the direction of acceleration in horizontal motion can vary.

  • How does the value of acceleration due to gravity change if we were on a different celestial body?

    -The value of acceleration due to gravity would be different if we were on a different celestial body because it depends on the particular mass and radius of the celestial body.

  • What is the significance of the negative direction in vertical motion?

    -In vertical motion, the negative direction is significant as it is always associated with the downward direction towards Earth, where objects accelerate due to gravity.

  • What are the two scenarios of vertical motion discussed in the script?

    -The two scenarios of vertical motion discussed in the script are objects in free fall (dropped downwards from a standstill) and objects with an initial upward velocity.

  • How long does it take for a rock to fall from a 100-meter tall cliff, and what is its velocity upon impact?

    -It takes approximately 4.5 seconds for a rock to fall from a 100-meter tall cliff, and its velocity upon impact is -44.1 m/s (negative because it is moving in the negative direction).

  • What happens to the velocity of a rock thrown straight up in the air due to Earth's gravity?

    -The velocity of a rock thrown straight up in the air will immediately begin to decrease due to the negative acceleration caused by Earth's gravity until it becomes 0, and then it will start to increase in the negative direction as it falls back down.

  • How long does it take for a rock thrown upwards with an initial velocity of 10 m/s to hit the ground?

    -It takes approximately 5.65 seconds for a rock thrown upwards with an initial velocity of 10 m/s to hit the ground.

  • What is the velocity of the rock at the point of impact when thrown upwards with an initial velocity of 10 m/s?

    -The velocity of the rock at the point of impact when thrown upwards with an initial velocity of 10 m/s is -45.4 m/s (negative because it is moving in the negative direction).

  • How do the equations for vertical motion differ when an object has an initial upward velocity?

    -When an object has an initial upward velocity, the equations for vertical motion involve a quadratic equation because there are both 't' and 't squared' terms. This requires using the quadratic formula to solve for the time 't'.

  • What is the main concept that the script emphasizes for understanding vertical motion?

    -The main concept emphasized in the script for understanding vertical motion is that it utilizes the same equations and concepts as horizontal motion, with the key difference being the constant acceleration due to gravity.

Outlines
00:00
πŸ“š Introduction to Vertical Motion

This paragraph introduces the concept of vertical motion, highlighting the familiarity with position, velocity, and acceleration, and how these relate to the kinematic equations. It emphasizes the constant acceleration due to Earth's gravity, which is -9.8 meters per second squared, and its uniqueness to Earth's mass and radius. The paragraph also discusses the directional convention for vertical motion, where 'down' is considered negative, contrasting with the arbitrary direction in horizontal motion. The discussion includes examples of free fall and objects with initial upward velocity, and how the acceleration remains -9.8 m/s^2 in both cases. A detailed calculation is provided for a rock dropped from a 100-meter cliff, including the time it takes to hit the ground and its velocity upon impact.

05:01
πŸš€ Calculating Time and Velocity in Vertical Motion

This paragraph delves into the application of kinematic equations to calculate the time and velocity of objects in vertical motion. It begins with the quadratic equation's application to find the time it takes for a rock thrown upwards to hit the ground, given an initial velocity and the acceleration due to gravity. The paragraph clarifies that the positive value for time is the one of interest, as negative time does not make physical sense. The calculated time for the rock's impact is 5.65 seconds, and its velocity is -45.4 m/s, indicating a slightly higher speed than the rock in free fall due to its initial upward trajectory. The summary underscores the consistent use of the same equations and principles for both upward and downward vertical motion, with gravity's constant acceleration being a key factor.

Mindmap
Keywords
πŸ’‘vertical motion
Vertical motion refers to the movement of an object along a vertical path, which is perpendicular to the Earth's surface. In the context of the video, it is the focus of the discussion, where the object's motion is influenced solely by gravity, resulting in a constant acceleration downwards at 9.8 m/sΒ². The video uses examples of a rock falling from a cliff and another thrown upwards to illustrate the principles of vertical motion.
πŸ’‘position
Position is a term used to describe the location of an object in relation to a reference point. In the video, position is one of the fundamental parameters discussed in relation to vertical motion, with the example of a rock falling from a cliff showing a change in position from an initial height to a final position on the ground.
πŸ’‘velocity
Velocity is a physical quantity that describes the rate of change of an object's position with respect to time, and includes both magnitude and direction. The video explains how velocity changes during vertical motion due to the constant acceleration of gravity, with the rock falling from the cliff starting at zero velocity and increasing as it falls, and the thrown rock starting with an upward velocity that decreases to zero before becoming negative as it falls back down.
πŸ’‘acceleration
Acceleration is the rate of change of velocity per unit time. In the context of the video, acceleration is constant for vertical motion due to Earth's gravity, with a value of -9.8 m/sΒ², indicating a downward direction. This constant acceleration is a key factor in calculating the motion of objects in the vertical direction, whether they are in free fall or thrown upwards.
πŸ’‘kinematic equations
Kinematic equations are mathematical formulas that relate position, velocity, and acceleration to time in the study of motion. In the video, these equations are used to predict the time it takes for an object to fall or return to the ground after being thrown, and to calculate the final velocity of the object at the moment of impact.
πŸ’‘free fall
Free fall is a type of motion where an object moves under the sole influence of gravity, starting from rest. The video uses the example of a rock dropped from a cliff to demonstrate the principles of free fall, highlighting how the object's velocity increases and the time it takes to hit the ground due to the constant acceleration of gravity.
πŸ’‘initial velocity
Initial velocity is the speed at which an object begins its motion in a particular direction. In the context of the video, the initial velocity is used to determine how the motion of an object thrown upwards differs from one that is simply dropped. The thrown rock has an initial upward velocity, which decreases due to gravity until it becomes zero, before the rock starts falling back down.
πŸ’‘Earth's gravity
Earth's gravity is the force that attracts two bodies towards each other, in this case, causing objects to experience a downward force. The video emphasizes that Earth's gravity is responsible for the constant acceleration of -9.8 m/sΒ² that objects experience during vertical motion, whether they are falling or thrown upwards.
πŸ’‘negative direction
The negative direction, in the context of the video, refers to the downward direction when discussing vertical motion. The acceleration due to gravity is always directed downwards, thus considered negative, and this affects how we analyze and calculate the motion of objects moving in the vertical direction.
πŸ’‘quadratic equation
A quadratic equation is a second-degree polynomial equation with one variable. In the video, the quadratic equation is used to solve for the time it takes for an object thrown upwards to fall back to the ground. The equation is rearranged into standard form and solved using the quadratic formula, which provides the time the object spends in the air before returning to its starting point.
πŸ’‘vector
A vector is a quantity that has both magnitude and direction. In the context of the video, velocity is described as a vector because it indicates not only how fast an object is moving but also the direction of its motion. The negative value of the final velocity for the falling rocks indicates that they are moving in the downward, or negative, direction at the time of impact.
Highlights

Professor Dave introduces the concept of vertical motion, relating it to familiar concepts like position, velocity, and acceleration.

Vertical motion differs from horizontal motion in that it involves Earth's constant acceleration due to gravity, -9.8 m/s^2.

The acceleration due to gravity is unique to Earth and would vary on different celestial bodies.

In vertical motion, the negative direction is consistently downward towards Earth.

Objects in free fall, starting from rest, experience the same acceleration due to Earth's gravity.

The time it takes for an object to fall from a height can be calculated using the position equation with an initial velocity of 0.

The velocity of a falling object at impact can be determined using the velocity equation with Earth's gravitational acceleration.

For an object thrown upwards, its initial velocity is opposite to the acceleration due to gravity, causing it to slow down and eventually fall back.

The time it takes for an object thrown upwards to land is longer than if it was simply dropped.

The quadratic equation is used to solve for the time of flight when an object is thrown upwards with an initial velocity.

The peak height of an object thrown upwards is greater than the initial height, affecting its final velocity upon impact.

Vertical motion equations and concepts are the same as horizontal motion, with the constant gravitational acceleration being the key difference.

The importance of careful arithmetic and understanding of signs is emphasized when solving vertical motion problems.

The tutorial provides practical examples, such as a rock falling from a cliff and another thrown upwards, to illustrate vertical motion concepts.

The final velocities of the rocks in both scenarios are negative, indicating the direction of motion is downward.

The tutorial concludes with a call to action for viewers to subscribe, support, and engage with Professor Dave for more content.

Transcripts

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