Podiatry

Projectile Motion:

Projectile motion: form of linear kinematics (curvilinear), shows changes in velocity and acceleration are going to occur once the object leaves the ground, hand, foot etc.
Linear motion that here are X & Y components, vertical and horizontal components.

Gravity:

Gravity results in constant vertical acceleration which is 9.8 m/s/s.
this does not affect horizontal velocity. Gravity and air resistance act on an object in air (air resistance is negligible).

Projectile Horizontal velocity component:

Horizontal velocity is constant (you end with what you start with).
Gravity plays no role in horizontal motion (ie. no acceleration)
Only displacement, velocity and time are the variables in horizontal velocity.
Acceleration only works vertically (ie. gravity -9.8m/s/s)

Projectile Vertical Velocity Component:

Vertical factor decreases as ball goes up and increases with ball coming down.
vertical velocity = 0 at peak.
The horizontal velocity remains that same (ignoring air resistance and no gravity/acceleration).
Vf (peak) = 0
time it takes for the ball to go up and down is the same as the time it takes for the ball to fly to the other side.
(Time of ball up and down = time of flight)


Projectile Vertical Velocity Component: 

Above diagram shows that there is no change in horizontal velocity.
There is an increase in vertical velocity as the ball comes down because it is affected by gravity/acceleration (-9.8m/s/s).
vertical component decreases as the bal goes up and increases as it comes down.
the gravity parabola occurs.

Key Concepts:

A projectile is any object upon which the only force is gravity.
Projectiles travel with a parabolic trajectory due to the influence of gravity.
There are no horizontal forces acting upon projectiles and thus no horizontal acceleration.
The horizontal velocity of  projectile is constant (a never changing in value).
There is a vertical acceleration caused by gravity, its value is 9.8m/s/s, down (negative).
The vertical velocity of a projectile changes by 9.8 m/s each second.
The horizontal motion of a projectile is independent of its vertical motion.
Centre of mass (CM) of projectile will travel in a parabolic path - regardless of the motion of the individual body segments.
Vertical velocity at the peak of the projectile's flight will b exactly zero.
Total Time up = Total time down (for same release and landing)

Factors influencing trajectory:

Release velocity.
Release angle.
Release height.

* air resistance is ignored.

Three factors (velocity, height, angle) determines how fast, high, long and far a projectile travels.


Release Velocity:

Most important factor in projectile motion.
Increase in speed of release (release velocity) increases two release parameters.
Increase in Vh increases distance Sh = Vh x t total.
Increase in Vv increases time of flight t total = 2 x Vv/g


Release Height:

Height only affects the time down.
Only a portion of one parameter is affected:
t total = t up + t down  - only t down is affected.


Release Angle:

Determines shape of trajectory. Trade off between Vv & Vh.
If 0 degrees = latter half of parabola. (if above landing height)

Release angle, height and speed interactions:

For any constant height: increase in speed results in optimum angle approaching 45 degrees.
For any constant speed, increase in release height results in decrease in optimum angle.
Velocity is Important! 

Theoretical Vs Optimal angles in Long Jump


Conversion of Vh to Vv

Running Sumersalt: Maintains the horizontal velocity while developing vertical velocity.
General Principles in throwing and hitting

Basketball and high jump.
Theory is 60 degrees but a practical angle is 50 degrees.


Basketball:

Velocity is the best variable to change for best results.

Equations of constant acceleration:



Outcomes:

Problems:

A baseball ball leaves the bat at 32.6m/s at an angle of 54 degrees. If the boundary fence is 8m from impact will the ball clear the fence?