Projectile Motion

Question 1

Projectile

Answer 1

Object in free-fall that is affected only by gravity and air resistance

Question 2

Trajectory

Answer 2

Flight path of a projectile

Question 3

Release

Answer 3

When object becomes a projectile

Question 4

Apex

Answer 4

Highest point of trajectory

Question 5

Primary Purposes in Projecting

Answer 5

Maximize horizontal distance (javelin, discus, shotput, long jump)

Maximize vertical height (High jump, pole vault)

Maximize Accuracy (archery, golf)

Maximize Accuracy when speed enhances effectiveness (football pass, baseball throw, tennis shot)

Maximize time in the air (gymnastics, figure skating, diving)

Question 6

Factors Influencing Projectile Motion

Answer 6

1. Relative height of release (projectile height)
   What height was projectile released?
   What height did projectile land?
2. Angle of release (projection angle)
3. .Velocity of release (projectile velocity)
   Magnitude of the velocity (= speed): how fast?

Question 7

Projectile Height

Answer 7

Given a constant projectile velocity & angle:
↑ projectile height → ↑ flight time → ↑ horizontal displacement

3 ways projectile height influences projectile motion

Question 8

Projection Angle

Answer 8

Influences shape of projectile’s trajectory
Projection θ = 90° → Vertical trajectory
vx = 0

Projection θ between 0-90° → Parabolic trajectory

Projection θ = 0° → latter ½ of parabolic trajectory
vy initial = 0

Question 9

Optimal Projection Angle?

Answer 9

Depends on goals of performance
Maximize vertical displacement → steep projection θ
Exp: high jump, pole vault
Maximize horizontal displacement → small projection θ
Exp: long jump, triple jump

Depends on projection height
Release Ht = Landing Ht → Optimal projection θ = 45 °
Exp: kick a ball for max horizontal displacement
Release Ht > Landing Ht → Optimal projection θ < 45 °
Exp: throw a ball for max horizontal displacement
Release Ht < Landing Ht → Optimal projection θ > 45 °
Exp: throw a ball onto elevated surface

Question 10

Projectile Velocity

Answer 10

Given a constant projectile angle & height:
Projectile velocity determines magnitude of vertical & horizontal displacement
velocity is a vector

velocity has a horizontal (vx) 
and vertical (vy) component

Question 11

Projectile Vertical Component

Answer 11

Vertical Component (vy)
Influences max vertical displacement (apex)
Constantly changing due to gravity

Question 12

Projectile Horizontal Component

Answer 12

Horizontal Component (vx)
Influences horizontal displacement (range)
Remains constant (assuming minimal air resistance)

Question 13

Importance of Velocity, Angle, and Height of Release

Answer 13

Projectile Velocity: most important
↑ vx → ↑ horizontal displacement (range)
↑ vy → ↑ time up & ↑ time down → ↑ total flight time

Projectile Height
↑ total flight time
↑ total flight time → ↑ horizontal displacement (range)
vx and vy remain same

Projectile Angle
Affects ratio of vx & vy
Minimal effect since ↑ in one are offset by ↓ in the other.

Question 14

Analyzing Projectile Motion

Answer 14

Equations of constant acceleration

Typically, equations are used to describe either horizontal or vertical motion