Revise: Motion in a Plane
Resolving and combining two-dimensional vectors, projectile motion, and the period, acceleration and force of circular motion.
vₓ = v cosθ, vy = v sinθ splits any angled vector into components.
20 m/s at 30°: vₓ ≈ 17.3 m/s, vy = 10 m/s.
Horizontal velocity stays constant; vertical velocity accelerates due to gravity.
A ball rolling off a table follows a curved (parabolic) path.
R = u²sin2θ/g; range is maximised at a 45° launch angle.
40 m/s at 45° gives R ≈ 163.3 m.
a = v²/r, always directed toward the centre — constant speed still means acceleration.
15 m/s around a 50 m curve gives a = 4.5 m/s².
F = mv²/r; a real force (tension, friction, gravity) must supply it — nothing pushes outward.
Earth's gravity supplies the centripetal force keeping satellites in orbit.
R = √(vₓ²+vy²), θ = tan⁻¹(vy/vₓ) recombines perpendicular components.
6 m/s and 8 m/s components combine to a 10 m/s resultant.
T = 2u sinθ/g; rise time equals fall time (symmetric motion).
25 m/s at 40° gives T ≈ 3.28 s.
H = u²sin²θ/2g; occurs when vertical velocity momentarily reaches zero.
14 m/s straight up gives H = 10 m.
T = 2πr/v (time per revolution); f = 1/T (revolutions per second).
5 revolutions in 2 s gives f = 2.5 Hz.