Free Fall and Motion Mechanics

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Questions and Answers

What is the initial velocity of a ball thrown downward from a window in the sample problem?

5.0 m/s

2.0 m/s (correct)

0 m/s

3.5 m/s

The maximum height of an object thrown upward has a velocity of zero.

True

What happens to the upward velocity of an object as it reaches its maximum height?

It decreases.

The acceleration due to gravity is approximately ____ m/s².

9.8 Signup and view all the answers

What is the final velocity before hitting the ground for an object thrown downward from a height of 2.5 m at 2.0 m/s?

-7.28 m/s Signup and view all the answers

Match the following terms with their descriptions:

Initial velocity = The starting speed of an object before any forces are applied Final velocity = The speed of an object just before impact Acceleration due to gravity = The rate at which an object's velocity increases due to Earth's gravitational pull Maximum height = The peak point an object reaches when thrown vertically upward Signup and view all the answers

An object thrown upward has a constant positive velocity throughout its ascent.

False Signup and view all the answers

What symmetry exists in the time taken for an object to ascend and descend?

The time going upward is equal to the time coming downward. Signup and view all the answers

What is the acceleration due to gravity used in free fall calculations?

9.8 m/s² Signup and view all the answers

A stone thrown downward from a height will always have a positive final velocity.

False Signup and view all the answers

Calculate the hangtime (T) for an object that takes 1 second to reach its maximum height.

1 s Signup and view all the answers

The distance covered when a stone falls from a 5-m high window after 0.5 seconds is _____ m.

5 Signup and view all the answers

What is the initial velocity (v_oy) of the stone thrown downward if it hits the ground at -7.55 m/s after falling for 0.5 s?

-2.45 m/s Signup and view all the answers

What formula is used to find the distance fallen (∆y) in free fall?

∆y = v_oy t + 0.5 g t² Signup and view all the answers

Match the following outcomes with their associated variables:

v_oy = Initial velocity during free fall g = Acceleration due to gravity T = Total time of flight ∆y = Vertical displacement Signup and view all the answers

The impact velocity of the stone just before it hits the ground is ____ m/s.

-7.55 Signup and view all the answers

What is the final velocity of the coin just before it hits the water?

-33.42 m/s Signup and view all the answers

What is the depth of the well determined from the time it took for the coin to hit the water?

56.63 meters Signup and view all the answers

Michael Jordan's takeoff speed was _____ m/s.

4.89 Signup and view all the answers

Which formula is used to calculate the final velocity of an object in free fall?

$v_{fy} = v_{0y} + gt$ Signup and view all the answers

The hangtime of an object in free fall is half the total time it takes to fall.

True Signup and view all the answers

Convert the height of Michael Jordan's leap from inches to meters.

1.22 Signup and view all the answers

Match the following values with their corresponding terms in the context of free fall:

0 m/s = Velocity at the highest point -9.8 m/s² = Acceleration due to gravity 4.89 m/s = Takeoff speed 3.41 s = Time of fall for the coin Signup and view all the answers

Study Notes

Free Fall

Free fall is uniformly accelerated motion under the sole influence of gravity
Objectives for understanding free fall include: defining free fall, describing a free-falling object's behavior, characterizing free fall's three cases, deriving kinematic equations for free fall, and solving free fall problems

Predicting the motion

A bowling ball and feather dropped simultaneously won't hit the ground at the same time in the presence of air resistance.
The bowling ball will fall faster due to its lower air resistance compared to the larger surface area of the feather

Debunking Common Myths

Heavier objects don't fall faster than lighter objects in a vacuum. Air resistance affects this outcome.
Objects with larger surface areas experience higher air resistance, resulting in slower fall rates compared to objects with smaller surface areas.
In a vacuum, objects of any mass fall at the same rate due to the absence of air resistance.

Key Features of a Free Falling Object

Acceleration due to Gravity:
- The only force acting on a free-falling object is gravity.
- Acceleration due to gravity (g) is approximately 9.8 m/s².
- Acceleration is directed downwards towards the Earth's center.
Time Symmetry (for objects thrown upwards):
- Time taken to reach the maximum height equals the time to return to the starting point.
Speed Symmetry (for objects thrown upwards):
- Speed of the object at any point on the way up equals the speed at the corresponding point on the way down, ignoring air resistance.
Velocities (for objects thrown upwards):
- Upward velocity is positive and decreasing.
- Downward velocity is negative and increasing.

Kinematic Equations for Free Fall

Kinematic equations for uniformly accelerated motion are adaptable to free fall, changing variables slightly.
The following table summarizes free fall quantities and their notation:

Quantity	Standard Symbol	Free-fall Symbol	Sign Conventions
Displacement	Δx	Δy	+(upward); -(downward)
Initial Velocity	v₀	v₀y	+ (above release point, upward); - (below release point, or when y is downward)
Final Velocity	vₙ	vₙy	+ (upward); - (downward)
Acceleration	a	g or aₙ	always negative (-)
Time	t	t	Time is a scalar quantity

Three Cases of Free Fall

Object Dropped at a Certain Height:
- Initial vertical velocity (Voy) = 0 m/s.
Object Thrown Downward:
- Non-zero negative initial velocity (i.e., Vo y< 0).
Object Thrown Upward:
- Non-zero positive initial velocity (i.e., Vo y> 0).

Sample Problems (Illustrative Examples)

Various examples using equations of motion to calculate different values such as the time taken to fall, maximum height, and final velocity, depending on different starting conditions. Specific values to each example are included in notes (e.g., initial velocity, acceleration, height)

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Description

This quiz explores the principles of free fall, including the effects of gravity and air resistance on falling objects. It covers the fundamental concepts of motion, the behavior of different objects during free fall, and debunks common myths surrounding this topic. Test your understanding of kinematic equations and real-world applications of these principles.