Applied Mathematics: Mechanics, Dynamics and Statistics
Applied Mathematics in Thanawiya Amma tests mechanics, dynamics and statistics. Mechanics questions check equilibrium and motion under forces; statistics questions check probability models and data interpretation.
Core rules
- Statics: resolve forces horizontally and vertically, take moments about a point, and apply ΣF = 0 and ΣM = 0 for equilibrium.
- Dynamics: Newton's second law F = ma; friction F = μN; projectiles separate horizontal uniform motion from vertical acceleration g.
- Probability: P(A or B) = P(A) + P(B) - P(A and B); independent events multiply; conditional probability uses P(A|B) = P(A and B)/P(B).
- Statistics: distinguish mean, median and mode; correlation measures linear association, not causation.
Worked example
A ball is projected at 20 m/s at 30° above the horizontal. Find its time of flight, taking g = 10 m/s². The vertical component is u_y = 20 sin 30° = 10 m/s. At landing the vertical displacement is zero, so t = 2u_y/g = 2 × 10/10 = 2 s. The horizontal component is not used because time depends on vertical motion.
Traps
- Using the total speed instead of its vertical component.
- Mixing sign conventions for upward and downward motion.
- Forgetting to resolve a force before applying equilibrium.
- Treating mutually exclusive events as independent.
- Reading correlation as proof of cause.