The document explains projectile trajectory, defined as the path followed by an object under the influence of various forces. Key factors affecting trajectory include initial velocity, angle of projection, projection height, air resistance, gravity, and spin. Additionally, it discusses how altitude impacts performance in athletic events, particularly highlighting the Olympic Games held at high altitude.

1. BY,
SARAN S
TRAJECTORY

2. WHAT IS TRAJECTORY?
THE PATH FOLLOWED BY A PROJECTILE
FLYING OR AN OBJECT MOVING UNDER
THE ACTION OF GIVEN FORCES.

5. FACTORS AFFECTING PROJECTILE TRAJECTORY
• INITIAL VELOCITY
• ANGLE OF PROJECTION
• PROJECTION HEIGHT RELEVENT TO THE LANDING SURFACE
• AIR RESISTANCE
• MASS
• VELOCITY
• GRAVITY
• SPIN
• SURFACE AREA OF THE PROJECTILE

6. INITIAL VELOCITY AFFECTING PROJECTILE
TRAJECTORY
• INITIAL VELOCITY IS DIRECTLY RELATED TO THE DISTANCE COVERED IN
FLIGHT. THE SPEED OF RELEASE DEPENDS ON A INITIAL VERTICAL
VELOCITY AND INITIAL HORIZONTAL VELOCITY. HAVING HIGHER
HORIZONTAL VELOCITY WILL INCREASE THE DISTANCE COVERED.

7. ANGLE OF PROJECTION AFFECTING
PROJECTILE TRAJECTORY
• AN OBJECT WHICH IS PROJECTED AT DIFFERENT ANGLES BUT THE
SAME INITIAL VELOCITY COVERS DIFFERENT DISTENCES.

8. PROJECTION HEIGHT RELEVENT TO THE LANDING
SURFACE
• HIGHER THE LEVEL OF RELEASE, LONGER THE DISTANCE IS COVERED
IN FLIGHT. THE HORIZONTAL COMPONENT WILL BE ACTING ON A
PROJECTILE FOR A LONGER DURATION, HENCE THE PROJECTILE WILL
BE COVERING A LONGER DISTANCE.

9. AIR RESISTANCE AFFECTING PROJECTILE
TRAJECTORY
• WHEN A PROJECTILE MOVES THROUGH THE AIR, IT IS SLOWED DOWN
BY THE AIR RESISTANCE
• AIR RESISTANCE DECRESE THE HORIZONTAL VELOCITY OF A
PROJECTILE.

10. GRAVITY AFFECTING PROJECTILE TRAJECTORY
• GRAVITATIONAL FORCEIS IS EXCERTED BY EARTH ON ALL THE OBJECTS
• GRAVITATIONAL FORCE IS CONSTANT FOR ALL THE OBJECTS
• GRAVITAIONAL FORCE DECREASES AT THE PLACES OF HIGH ALTITUDE
• PERFORMANCE IN JUMPS AND THROWS IS BETTER AT THE PLACES OF
HIGH ALTITUDE
The Olympic Games in Mexico were
controversially held at the highest altitude
ever. The venue had an altitude of 2,239
meters (7,349 feet). The thin air was bad for
athletes in endurance events, but it lead to
records in short races, relays, and jumping
events

11. SPIN AFFECTING PROJECTILE TRAJECTORY
• AMOUNT AND DIRECTION OF SPIN DIRECTLY AFFECTS THE DISTANCE
COVERED
• IF THE SPIN CREATES LOW PRESSURE ON THE TOP, THE OBJECT
REMAINS IN THE AIR FOR LONGER PERIOD COVERING LONGER
DISTANCE
• IF THE OBJECT CREATES HIGH PRESSURE ON THE TOP, THE OBJECT
REMAINS IN THE AIR FOR SHORTER PERIOD AND COVERS SHORTER
DISTANCE

12. EQUATION OF
TRAJECTORY
0
10
20
30
40
50
0 1 2 3 4 5 6 7
x=u cosθ
Y=u
sinθ
u
θ
X= u cosθ t +
1
2
a x 𝑡2
Since horizontal component of acceleration is always 0
X= u cosθ t --------- ①
Y= u sinθ t -
1
2
g 𝑡2
--------②
If we eliminate time t
X= u cosθ t :therefore t=
𝑥
𝑢 𝑐𝑜𝑠θ
Where: y= u sinθ
𝑥
𝑢 𝑐𝑜𝑠θ
−
1
2
𝑔
𝑥
𝑢 𝑐𝑜𝑠θ
𝑥2
: y= x tanθ -
1
2
𝑔 𝑥2
𝑢2 𝑐𝑜𝑠2 θ

13. THANKYOU