Deriving Projectile Formulae (AQA A-Level Mathematics): Flashcards

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Deriving Projectile Formulae
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Horizontal component of initial velocity (uxu_x)

ux=ucos⁡θu_x = u \cos \theta

Vertical component of initial velocity (uyu_y)

uy=usin⁡θu_y = u \sin \theta

Horizontal acceleration in projectile motion (axa_x)

ax=0a_x = 0

Vertical acceleration in projectile motion (aya_y)

ay=−ga_y = -g

Horizontal displacement formula for projectile

x=(ucos⁡θ)tx = (u \cos \theta) t

Vertical displacement formula for projectile

y=usin⁡θ⋅t−12gt2y = u \sin \theta \cdot t - \frac{1}{2} g t^2

Time of flight formula (TT)

T=2usin⁡θgT = \frac{2u \sin \theta}{g}

Maximum height formula (HH)

H=(usin⁡θ)22gH = \frac{(u \sin \theta)^2}{2g}

Range formula (RR)

R=u2sin⁡2θgR = \frac{u^2 \sin 2\theta}{g}

Vertical velocity at maximum height (vyv_y)

vy=0v_y = 0

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