| 1.1.2 Scalars, Vectors and Projectile Motion |
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Key Definition Scalar quantities are described by magnitude alone, while vector quantities require both a magnitude and a direction.
Vectors are represented by arrows whose length encodes the magnitude and whose direction encodes the orientation of the quantity.
Any vector can be resolved into two perpendicular components using:
$F_{\mathrm{x}}$ = F cos θ $F_{\mathrm{y}}$ = F sin θ
where the angle θ is measured from the horizontal.
The reverse process — recombining two perpendicular components into a single vector — uses Pythagoras' theorem to find the magnitude and the tangent ratio to find the direction.
Key Definition The resultant of two vectors is the single vector that has the same effect as the two vectors acting together.
For perpendicular vectors, the resultant is found by calculation; for vectors at any other angle, it can be found by scale drawing or by resolving each vector into perpendicular components and recombining them.
Projectile motion
Projectile motion treats the horizontal and vertical motions as independent, since gravity acts only in the vertical direction.
The horizontal velocity remains constant when air resistance is neglected, because there is no horizontal force acting.
The vertical motion is uniformly accelerated downwards at g (approximately 9.81 m s⁻²).
- Resolve the initial velocity into its horizontal and vertical components.
- Apply the suvat equations to the vertical direction to find the time of flight.
- Use that time in the horizontal direction to find the range.
At the peak of the trajectory, the vertical component of velocity is momentarily zero, but the horizontal component is unchanged.
Exam Tip Always state both a magnitude and a direction for vector quantities, and define a positive direction before carrying out any sign-sensitive calculation.