KHS Lecture 9: Velocity, Acceleration, and Projectiles

Velocity

• Average velocity = displacement / time (m/sec)

- Vector quantity

Baseball, reaction time of a hitter needed to hit a pitch of 90 mph from 60.5 feet (the ball is released 2.5 feet in front of mound)

- Calculate time

0.44 seconds

Application: GPS/LPS - Player Load Monitoring

Uses combo of inertial measurement units (accelerometers, magnetometer, gyroscopes) & satellites to triangulate athlete's position - 10 Hz

• Running/cycling distance, velocity/speed, acceleration, deceleration, jumps, COD, impact

Load Monitoring

Internal (RPE, HR, BP, HRV, biochem markers)

Vs.

External (key performance indicators [KPI])

- Tracking software daily, weekly, monthly, yearly

Internal Load Monitoring

RPE, HR, BP, HRV, biochem markers

External Load Monitoring

key performance indicators (KPI)

Acceleration

rate of change of velocity

- Object accelerates when it speeds up, slows down, starts, stops, & changes direction

- Instantaneous versus average acceleration

Acceleration equation

a=vf-vi/t

Vf

final velocity

Vi

initial velocity

t

time

Is Acceleration directional?

No, only + or -

- Instantaneous versus average acceleration

Explain Pelvic Acceleration with a progression that increases with difficulty

The more difficult the progression, the greater the pelvic ACC

Projectile Examples

Human body and objects

Uniform Acceleration: Projectiles

- constant net external force acting on an object with vertical motion being constant

- an object that has no external forces acting on it other than gravity

- Vertical motion is a constant: g = -9.81 m/s^2

Law of Inertia

horizontal velocity component is constant

Vertical Velocity

will change from + at release, to 0 peak, and - upon return

Vpeak

0 m/s

Horizontal Acceleration

0 m/s^2

Vertical Acceleration

-9.81 m/s^2

Projectile Calculations

Vertical position

Vertical velocity

Horizontal velocity

Horizontal position

Vertical & horizontal displacement

Flight time

Vf = Vi + gΔt

Solve for projectile’s final velocity

- a = Vf – Vi / Δt will also be = g

- Vf – Vi = g Δt

1st Law of Uniformly Accelerated Motion

A projectile's final velocity is related to its Initial velocity & constant acceleration

Vf^2 = Vi^2 + 2gΔy

If vertical displacement is known

3rd Law of Uniformly Accelerated Motion

A projectile's final velocity is related to its acceleration & displacement

Vf = (g)(Δt)

or

Vf^2 = 2g(Δy)

If an object is free falling (Vi = 0m/s)

Vi^2 = 2g(Δy)

if an object is thrown up (Vf = 0 m/s)

2nd Law of Uniformly Accelerated Motion

A projectile's final position is related to its initial velocity & acceleration

yf = yi + (vi)iΔt - (1/2)g(Δt^2)

solving for vertical position

yf = ½(g)(Δt)^2

Free falling objects (yi, vi = 0)

ΔY = (Vr ∙ sinƟ)^2 / 2g

if the projectile is released at an angle instead of directly upward

Tup = resultant v (sinθ)= / g

Solve for flight time when resultant velocity & angle are known

Total flight time = 2(timeup)

Tup = Tdown : landing & release heights :

SQRT(2gx + (vsinθ)^2 / g^2)

When landing & release ht differ

Vh x Δt

horizontal displacement

xi + Vh(Δt)

horizontal position

Range

total horizontal displacement of a projectile

v^2 x sin2Ɵ / g

range on a flat ground

v^2 ∙ sinƟ ∙ cosƟ ∙ + x ∙ SQRT((Vy^2) + 2gh) / g

Range when projectile is released from elevated height (h)

Optimal angle if release height = landing

45°

Optimal angle if landing height is lower than release

less than 45°

Optimal angle if landing height is higher than release

greater than 45°

Max vertical height

closer to 90°

When is a 45° angle optimal

if there is an equal need for vertical and horizontal velocity

What affects optimal angle?

angle affected by Vv and Vh at release

Projection Speed of Implement decreases if:

projection angle increase

What's more critical, projection speed or angle?

projection angle

Optimal angle of shotput

26-42°

Average angle of shotput

37°

Optimal angle of Javelin

about 32-36°

Optimal Angle of Long Jump

18-27 degrees

- take off angle decreases as velocity increases

Discus (Opt, Avg, Deviation)

Opt Angle: 35-40°

Average: 35°

2° deviation = decrease 0.2m in distance

5° deviation = decrease 1.26m in distance

High Jump optimal angle

approached from a 40-48° angle

Soccer Throw-in

Optimal Angle: 30°

- Distance of throw may increase by a few meters by using fast backspin, but ball must be launched at a slightly lower release angle

Baseball Swing

35°

- Ball arrives 10° downward trajectory

- Hitter Swings at 25°

Golf Drive

Depends on many factors such as club head velocity, ball velocity, spin rate, loft angle, backspin, drag & lift force

- Avg PGA TOUR player = launch angle of 11.2° &spin rate of 2,685 rpm

- Contact time < 0.5 ms, swing speeds > 120mph, forces > 5 kNmph, forces > 5 kN

- Loft Angle

Loft Angle

angle clubface makes with the vertical when club head impacts ball

Projection of Accuracy

Balance between projection angle, velocity, release & landing height, distance from target, &barriers

•Small projection angle = ↑ horizontal component & ↓ flight time

•Large projection angle = ↓ horizontal component & ↑ flight time

Small Projection Angle

↑ horizontal component & ↓ flight time

Large Projection Angle

↓ horizontal component & ↑ flight time

Optimal Angle for a jump shot

52 degrees

- (ranges from 49-55 degrees)

- angle may increase closer to rim

How to convert mph to ft/s and vise versa

1 mph = 1.47 ft/s

1 ft/s = 0.68 mph