M1 – Projectiles Summary
M1 – Projectiles Summary
 Modelling assumptions: No air resistance– gravity is the only force
acting and the ground is a level plane
 Modelling assumptions: No air resistance– gravity is the only force
acting and the ground is a level plane
Throughout the flight of a projectile
 Horizontal acceleration = 0 ms-2 and vertical acceleration = g ms-2
 Since the acceleration is constant the suvat equations apply in both the
horizontal and vertical directions
 To calculate time of flight use vertical displacement = 0 m.
 If the projectile is released from the same height as it lands, its path is
symmetrical.
 At its maximum height the vertical velocity = 0 ms-1. (When the particle is
released from the same height as it lands, this is halfway through the
flight.)
 Range is the horizontal distance travelled. To find the range calculate
horizontal displacement at the time when the particle lands.
 Horizontal velocity is constant throughout the flight.
 To find the speed and direction of the projectile at any time use
Pythagoras and trigonometry on the components of v
 Remember, at the maximum height the vertical component of velocity is
zero. This is the time when the projectile has its least speed.
 If the object is released from a height h the same motion will occur but
take the height of release is the origin. (When the projectile lands on the
ground the vertical displacement = h.)
Throughout the flight of a projectile
 Horizontal acceleration = 0 ms-2 and vertical acceleration = g ms-2
 Since the acceleration is constant the suvat equations apply in both the
horizontal and vertical directions
 To calculate time of flight use vertical displacement = 0 m.
 If the projectile is released from the same height as it lands, its path is
symmetrical.
 At its maximum height the vertical velocity = 0 ms-1. (When the particle is
released from the same height as it lands, this is halfway through the
flight.)
 Range is the horizontal distance travelled. To find the range calculate
horizontal displacement at the time when the particle lands.
 Horizontal velocity is constant throughout the flight.
 To find the speed and direction of the projectile at any time use
Pythagoras and trigonometry on the components of v
 Remember, at the maximum height the vertical component of velocity is
zero. This is the time when the projectile has its least speed.
 If the object is released from a height h the same motion will occur but
take the height of release is the origin. (When the projectile lands on the
ground the vertical displacement = h.)
When the two components are combined these result in the following
formulae:
 a = gj
 v = ucosI + (usin  gt)j
 r = utcosi + (utsin  12 gt2 + h)j
When the two components are combined these result in the following
formulae:
 a = gj
 v = ucosI + (usin  gt)j
 r = utcosi + (utsin  12 gt2 + h)j
where u is the initial speed,  is the angle of projection and h is the height of
release.
where u is the initial speed,  is the angle of projection and h is the height of
release.