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

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Deriving Projectile Formulae
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Air resistance in projectile motion

Neglected (ignored)

Type of horizontal motion in projectiles

Constant velocity

Type of vertical motion in projectiles

Constant acceleration due to gravity

Formula: horizontal component of uu

ux=ucos⁡θu_x = u \cos \theta

Formula: vertical component of uu

uy=usin⁡θu_y = u \sin \theta

Horizontal acceleration axa_x

ax=0a_x = 0

Vertical acceleration aya_y

ay=−ga_y = -g

Formula: horizontal displacement

x=(ucos⁡θ)tx = (u \cos \theta) t

Formula: vertical displacement

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

Formula: vertical velocity

vy=usin⁡θ−gtv_y = u \sin \theta - gt

Formula: time of flight TT

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

Formula: maximum height HH

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

Formula: range RR

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

Vertical velocity at max height

vy=0v_y = 0

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