Projectile Motion
Motion of a body thrown at an angle near the Earth's surface, with constant horizontal velocity and constant vertical acceleration g.
What is Projectile Motion?
Motion of a body thrown at an angle near the Earth's surface, with constant horizontal velocity and constant vertical acceleration g.
Key formula / rule: Horizontal: a = 0; vertical: a = -g.
Key points
- Derive range, maximum height and time of flight for a projectile.
- Apply projectile relations to a launch on level ground.
- Analyse how drag alters the ideal parabolic trajectory.
Common exam trap
Using g in the horizontal direction.
Definitions
- Term
Projectile Motion
- Meaning
Motion of a body thrown at an angle near the Earth's surface, with constant horizontal velocity and constant vertical acceleration g.
- Term
Projectile Motion — explanation
- Meaning
The horizontal and vertical motions are independent and share only the time variable. Range R = u2 sin 2t / g, maximum height H = u2 sin2 t / 2g and time of flight T = 2u sin t / g follow directly from the one-dimensional equations applied to each axis.
Learning objectives
Derive range, maximum height and time of flight for a projectile.
Apply projectile relations to a launch on level ground.
Analyse how drag alters the ideal parabolic trajectory.
Formulae
- Key point
Horizontal: a = 0; vertical: a = -g.
- Key point
R is maximum at 45 degrees; complementary angles give the same range.
- Key point
The trajectory is a parabola for constant g and no drag.
Prerequisites
PHY-U1-KIN-T2-S1-C2
PHY-U1-KIN-T1-S2-C3
Common mistakes
Using g in the horizontal direction.
Assuming speed is zero at the highest point; only the vertical component vanishes.
Keywords
Projectile
Motion
Practice preview
A projectile is launched with an initial velocity of 20 m/s at an angle of 45 degrees with the horizontal. What is its horizontal range? (Take g = 10 m/s^2)…
easy
A projectile is thrown such that its horizontal range is 4 times its maximum height. What is the angle of projection?…
medium
A projectile is launched with an initial velocity of 50 m/s at an angle of 37 degrees with the horizontal. What is its speed after 3 seconds? (Take g = 10 m/s^2, sin(37) = 0.6, cos(37) = 0.8)…
medium