An easy way to understand 'Projectile Motion'

1. Name: Umair Islam
Topic: Projectile Motion

2. Projectile motion
Projectile Motion
Two dimensional motion under constant
gravitational acceleration is called projectile
motion.
EXAMPLES OF PROJECTILES:
(1) A missile shot from a gun
(2)A bomb released from a bomber
(3) Kicked or thrown balls
(4)Jumping of animals
(5)Object thrown from a window are some examples
of projectile.

3. To analyze projectile motion following three assumptions are
made.
(1) The acceleration due to gravity is constant over the range of
motion and is directed downward.
(2) The medium of projectile motion is assumed to be non-
resistive (i.e. air resistance is negligible).
(3) The rotation of earth does not affected the motion.
Equation of Trajectory
The path adopt by the projectile is called
trajectory.
Consider a projectile having mass m is projected at
a point in xy-plane with initial velocity which makes
angle with x-axis.

5. There are two component of velocity
The position of projectile at any time t is

6. Two forces act on the projectile
(1)Gravitational Force
(2) Air Resistance
Neglecting the air resistance, then gravitational
force acting vertically downward is
Also

7. On comparing equation (iii) and (iv)
By separating variables, equation (v) becomes
Integrating equation (vi)
…….(vi)

8. Where c is integration constant and its value can be
determined from initial boundary conditions.
At
By separating variables, equation (vii) becomes

9. Integrating, equation (viii)
Putting value of
Compare (ii) and (ix)

10. Comparing coefficients
The value of t from (x) is
Putting value of t in (xi)

12. Range of Projectile
The distance along x-axis between point of
projection and point of landing is called range
of projectile.

13. Its value can be calculated as
The equation of trajectory of projectile is
Put y=0 for point of projection and point of
landing.

14. And

15. 𝑅 =
𝑣 𝑜
2 sin 2𝛼
𝑔
𝑅 =
𝑣 𝑜
2 sin 2𝛼
𝑔
− 0

16. The range of projectile will be maximum when
When projectile is projected at angle the range of projectile will
be maximum.

17. Time of Flight
The time taken by the projectile between point
of projection and point of landing is called
time of flight. It is denoted by T.
The equation of motion of projectile in vertical
direction is
Put y=0

19. Height of projectile
The maximum distance reached by projectile
in vertical direction is called maximum height
and denoted by H.
The equation of motion of projectile in vertical
direction is
Time of flight is

20. But time to reach at maximum height is half
the time of flight.
Putting value of t in equation (i)

22. Thank You