Biomechanics Final Exam Review: Projectile Motion
Acceleration due to Gravity
*-9.81 m/s ^2*. -The acceleration of an object in free fall that results from the influence of the Earth's gravity. -Remains *constant* in a free-fall [where no other forces are acting].
When a ball is thrown straight up, its velocity is going in a *Positive*, upward, direction. But velocity is *Decreasing* as the ball continues to rise. As the ball's trajectory reaches its apex, the ball's velocity is instantaneously *Zero*. As the ball falls downward, or in a *Negative* direction, it's speed is *Increasing*. WHY?
*Acceleration remains constant* at -9.81 meters per second squared. Since *gravity* is the only force acting on the ball. *(-9.81 m/s^2)*
Projection Angle has direct implications for success in what sport?
*Basketball.* -A nearly vertical angle of entry into a basket allows for greater margin of error than a horizontal angle's entry. -Novice players often shoot with an angle thats too horizontal, creating a more flat trajectory. --Jump Shot Release: [52 to 55]. --When Being Blocked: [More Vertical, Higher Release.]
When a ball is thrown straight up, its velocity is going in a ___, upward, direction. The velocity is ___ as the ball continues to rise.
*Positive* direction. Velocity is *decreasing* as the ball rises.
When a ball is thrown straight up, its velocity is going in a ___, upward, direction. But it is ___ as the ball continues to rise. At the ball's trajectory reaches its apex, the ball's velocity is instantaneously ___.
*Positive* direction. Velocity is *decreasing* as the ball rises. The ball's velocity at apex is instantaneously *zero*.
A projectile's ___ is the product of its horizontal speed and flight time. Aka, the ___ ___ of a projectile at Landing.
*Range.* [Horizontal distance]. The *Horizontal Displacement* of a projectile at Landing.
What Determines the Length or Size of a projectile's trajectory?
*The Projection Speed*. [When projection angle and other factors are constant.] a.) *Projected Vertically*: determines *height* of the apex. b.) *Projected Obliquely*: determines both the *height* and the *horizontal length* of a trajectory.
A skydiver's vertical velocity [with air resistance], becomes ___ once the parachute opens.
*Vertical velocity becomes much smaller* than before the parachute was opened.
Initial Velocity
-A vector quantity. -Incorporates *Angle of Projection*, and *Initial Speed*. -Both the Horizontal and Vertical Components have their own velocities. [Vh, Vv]. Together they make the *Resultant Initial Velocity*, [V].
The Relative Height of Projection
-Difference between projection height and landing height. [Projection Height - Landing Height = Relative Projection Height.]
The Projection Speed
-The *Magnitude of projection Velocity*. -Determines the *Length* or *Size* of a projectile's trajectory. [When projection angle and other factors are constant.] a.) *Projected Vertically*: determines *height* of the apex. b.) *Projected Obliquely*: determines both the *height* and the *horizontal length* of a trajectory.
What are the three main, mechanical factors that influence the trajectory of a projectile?
1. *The Angle of Projection*: the direction, with respect to the horizontal, at which a body is projected. Determines the *shape* of the trajectory. *a.)* Vertical Projection Angle: Vertical trajectory. *b.)* Oblique Projection Angle: [between 0 and 90°]: Parabolic trajectory. *c.)* Horizontal Projection Angle: [0°]: One-half of a parabola. 2. *The Projection Speed*: the magnitude of projection velocity. Determines the *length* or *size* of a projectile's trajectory. [When projection angle and other factors are constant.] *a.)* Projected Vertically: determines *height* of the apex. *b.)* Projected Obliquely: determines both the *height* and the *horizontal length* of a trajectory. 3. *The Relative Height of Projection*:
Body in free fall that is subject only to the forces of gravity and air resistance
A Projectile.
A Vertical Projection Angle will create what type of trajectory?
A Vertical Trajectory, straight up and down.
If a ball is thrown vertically, its *acceleration remains ___* at *[-9.81 m/s^2],* since ___ is the only force acting on the ball.
Acceleration remains *Constant.* Since *Gravity* is the only force.
The highest point in the trajectory of a projectile, right between going up and down.
Apex
Why are airplanes and rockets not considered projectiles
As long as an object is moving through the air unassisted, they can be considered a projectile. [Other than the forces of gravity and air resistance]. Therefore they can not be a projectile, they are influenced by forces generated by their engines.
Optimum Angle of Projection
Based on Relative Projection Height. Used to reach the maximum horizontal displacement in most sports. -When the RPH is equal to *zero*, the OAP is *45°*. -As the RPH *increases*, the OAP *decreases*. -As the RPH *decreases*, the OAP *increases*.
What is a Projectile?
Body in unassisted free-fall that is subject only to the forces of gravity and air resistance.
To land as close to their targets on the ground, skydiver's utilize ___?
Both horizontal and vertical components of velocity.
A projectile's Flight Time is increased by what?
By increasing the vertical component of projection velocity, or by increasing the relative projection height. -Keep in air longer, longer fall time
An object in free fall experiences
Constant Acceleration
The Horizontal Component relates to the ___ ___ by the projectile
Distance Traveled.
A projectile's ___ ___ is increased by increasing the vertical component of projection velocity, or by increasing the relative projection height
Flight Time
Trajectory
Flight path of a projectile
Laws of Constant Acceleration
Galileo's formulas relating: -*Displacement*, d. -*Velocity*, v. [Vi and Vf]. -*Acceleration*, a. -*Time*, t. [When acceleration is unchanging.] [Apply to vertical and horizontal components].
The Vertical Component of a projectile is influenced by what?
Gravity
Vertical and Horizontal components of Projectile Motion are ____
Interdependent. [A ball hit horizontally has the same vertical displacement as a ball dropped with no horizontal velocity.]
Galileo's 3 laws
Laws of Constant Acceleration
The Vertical Component relates to the ___ ___ ___ by the projectile
Maximum Height Achieved. {projection speed}
No force, neglecting ____, can influence a projectile's ____ Component.
Neglecting air resistance. The Horizontal Component
The Horizontal Component is influenced by what?
No force, [neglecting air resistance], can influence a projectiles horizontal component.
The Projection Speed, if a projectile is projected Vertically, will determine a trajectory's ___?
determines a trajectory's *Height* at the Apex.
The Projection Speed, if a projectile is projected at an Oblique angle, will determine a trajectory's ___ and ___?
determines both the *height* and the *horizontal length* of a trajectory. [Between 0 to 90° projection angle].
As the RPH ___, the OAP decreases.
increases
If a driven golf ball becomes lodged in a tree, the relative projection height is ___, because the landing height is ___ than the projection height.
the relative projection height is *Negative*. Landing height is *Greater* than the projection height. -[PH = .1 meters]. -[LH = 1.1 meters]. -[PH-LH=RPH]. --- Relative Projection Height = [ .1 - 1.1 = -1 meters ]
When a ball is thrown straight up, its velocity is going in a ___, upward, direction.
Positive
Success in Basketball has a lot to do with the ___ ___ players use to shoot the ball.
Projection Angle. -A nearly vertical angle of entry into a basket allows for greater margin of error than a horizontal angle's entry.
Formula for The Relative Height of Projection.
Projection Height - Landing Height = Relative Projection Height. PH - LH = RPH.
Based on Relative Projection Height. Used to reach the maximum horizontal displacement in many throwing sports
Projection Speed, and The Optimum Angle of Projection.
Used to reach the maximum vertical and horizontal displacement in most sports.
Projection Speed. [More important than Projection height].
The Optimum Angle of Projection = 45°
Relative Projection Height = 0.
Shot Put, Javelin Throw, and Discus Throw distance is determined by the ___ ___ ____ of the projectile
Resultant Horizontal Displacement
The pattern of change in the vertical velocity of a projectile is ___ on each side of the apex
Symmetrical, opposite direction
A Projectile's Range
The *Horizontal Displacement* of a projectile at Landing. The product of a projectile's: 1. *Horizontal Speed*. and 2. *Flight Time*.
The direction, with respect to the Horizontal, at which a body is projected. Determines the Shape of the trajectory.
The Angle of Projection
What determines the Shape of a trajectory?
The Angle of Projection/Projection Angle.
Relates to the Distance Traveled by a projectile.
The Horizontal Component.
If the Relative Projection Height, RPH, = 0
The Optimum Angle of Projection = 45°
What determines a trajectory's height at the apex.
The Projection Speed, if it is projected *Vertically*.
What determines both the height and the horizontal length of a trajectory?
The Projection Speed, if it is projected at an *Oblique Angle*.
The Horizontal Displacement of a projectile at Landing is known as the ___ of a projectile.
The Range of a projectile. [Distance]
Difference between projection height and landing height.
The Relative Height of Projection.
A ball hit horizontally has ___ ___vertical displacement as a ball dropped with no horizontal velocity.
The Same.
Gravity influences which component of projectile motion?
The Vertical Component.
Relates to the maximum height achieved by a projectile.
The Vertical Component. Projection speed, if projected Vertically.
Flight Time
The amount of time that a projectile is in the air.
If a ball is caught at the same height from which it was tossed, the balls speed would be ____ as its initial speed, although its ___ would have changed.
The ball's speed would be: *the exact same.* Its direction, [positive or negative], would be: *reversed*, or *opposite* of the initial.
The Angle of Projection
The direction, with respect to the *horizontal*, at which a body is projected. Determines the *Shape* of the trajectory. a.)* Vertical Projection Angle*: Vertical trajectory. b.)* Oblique Projection Angle*, [between 0 and 90°]: Parabolic trajectory. c.)* Horizontal Projection Angle*, [0°]: One-half of a parabola.
A ball thrown with a given initial velocity in an outdoor arena will travel much farther if it is thrown in which type of wind? [Air Resistance]
The distance of the projectile will be *further if it it thrown with a tailwind,* versus a headwind. [Horizontal velocity].
Motion
The effect of force.
Apex
The highest point in the trajectory of a projectile. Right in-between going up and down, vertical velocity= 0.
The horizontal acceleration of a projectile is always ___. The horizontal velocity of a projectile is always ___.
The horizontal acceleration is always *Zero*. Horizontal Velocity is always *Constant*.
Which of the components of a projectiles flight remains constant throughout the trajectory?
The horizontal component, [distance]. [When there is no air resistance.]
A projectile's range is the product of its ___ and ___.
The product of a projectile's: 1. *Horizontal Speed*. and 2. *Flight Time*. [Range = The *Horizontal Displacement* of a projectile at Landing. [horizontal distance].
High Jumpers and Pole Vaulters maximize ___ ___ ___ to win events.
Ultimate Vertical Displacement.
As long as an object is moving through the air ____, they can be considered a projectile
Unassisted. [Other than the forces of gravity and air resistance].
When a ball is thrown straight up, its velocity is going in a ___, upward, direction. But velocity is ___ as the ball continues to rise. As the ball's trajectory reaches its apex, the ball's velocity is instantaneously ___. Vertical velocity, as the ball falls downward, or in a ___ direction, it's speed is ___.
Upward, *Positive* direction. Velocity is *Decreasing* as the ball rises. The ball's velocity at apex is instantaneously *Zero*. Ball falls Downward, in a *Negative* direction. It's speed is *Increasing*.
Vertical speed of projectiles are always changing, due to ___ ___. Vertical acceleration is ___.
Vertical Speed is changing, Due to gravitational acceleration. Vertical acceleration is constant, -9.81
Give an explanation of the trajectory of a projectile, [a ball], concerning its *Vertical Velocity*.
When a ball is thrown straight up, its velocity is going in a *Positive*, upward, direction. But velocity is *Decreasing* as the ball continues to rise. As the ball's trajectory reaches its apex, the ball's velocity is instantaneously *Zero*. Vertical velocity, as the ball falls downward, or in a *Negative* direction, it's speed is *Increasing*.
Explain how to get maximum horizontal displacement, using the Optimum Angle of Projection
When release height is 0 then angle that produces max horizontal displacement is 45°. As relative projection height increases, the optimum angle of projection decreases.
At the peak, or apex, of the flight Vertical Velocity =
Zero
A Horizontal Projection Angle will create what type of trajectory?
[0° angle of projection.] Will create One-Half of a Parabolic Trajectory
An Oblique Projection Angle will create what type of trajectory?
[Between 0 to 90° angle of projection]. Will create a Parabolic Trajectory
Horizontal Displacement aka
aka Range, or horizontal distance traveled.
What are the 2 main components of projectiles?
1. The Vertical Component. 2. The Horizontal Component.
The product of a projectile's ___ and ___ determine the Horizontal Displacement, or Range of a projectile.
Horizontal Speed and Flight Time
The ___ acceleration of a projectile is always *zero*, and the ___ of the projectile is always *Constant*.
Horizontal acceleration, = 0. Velocity is Constant.
