MATHEMATICAL FORMULAE
Further Mechanics
Motion of a projectile
The range, xmax/R is:
xmax
u2 sin 2θ
=
g
ymax
u2 sin2 θ
=
g
The maximum height, ymax/H is:
The time of flight, T is:
T=
2u sin 𝜃
g
Equation of trajectory is:
y = x tan 𝜃 −
gx2
2u2 cos2 𝜃
Note that this is applicable if g opposes the motion. If g is in the direction of motion, then:
y = x tan 𝜃 +
gx2
2u2 cos2 𝜃
For displacement:
x = ut cos θ
1
y = ut sin θ − at2
2
Note that for y this is applicable if g opposes the motion. If g is in the direction of motion, then:
1
y = ut sin θ + at2
2
For velocity:
vx = u cos θ
vy = u sin θ − gt
Note that for vy this is applicable if g opposes the motion. If g is in the direction of motion, then:
vy = u sin θ + gt
Angle of projection is:
tan θ =
vy
vx