How do you resolve initial speed u at angle \alpha?

Horizontal u\cos\alpha, vertical u\sin\alpha.

What is the horizontal acceleration of a projectile?

Zero, so the horizontal velocity is constant.

Range from level ground?

R=u\cos\alpha\times T=\dfrac{u^2\sin2\alpha}{g}

How do you find the speed at a given time?

\sqrt{vx^2+vy^2}, with vy=u\sin\alpha-gt.

How do you find the direction of motion?

\tan\phi=\dfrac{|vy|}{|vx|} and the sign of vy gives up or down.

Which root of a quadratic in t do you take?

The positive one, since time cannot be negative.

How can you find the time to hit the ground from a height?

Use s=ut+\tfrac12at^2 vertically with the negative displacement and solve the quadratic.

What sign convention should you state?

For example 'upwards is positive', so a=-g.

Motion in a vertical plane and projectilesEdexcel International A Level Further Maths: Flashcards

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What assumptions does the projectile model make?

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What assumptions does the projectile model make?: Particle; no air resistance; constant $g$ downwards; no other forces.
What value of g is used in Edexcel IAL Mechanics?: $9.8\text{ m s}^{-2}$
How do you resolve initial speed $u$ at angle $\alpha$ ?: Horizontal $u\cos\alpha$ , vertical $u\sin\alpha$ .
What is the horizontal acceleration of a projectile?: Zero, so the horizontal velocity is constant.
What is the vertical acceleration of a projectile?: $g=9.8\text{ m s}^{-2}$ downwards.
What is the vertical velocity at the greatest height?: Zero ( $v_y=0$ ).
Time of flight from level ground?: $T=\dfrac{2u\sin\alpha}{g}$
Greatest height from level ground?: $H=\dfrac{u^2\sin^2\alpha}{2g}$
Range from level ground?: $R=u\cos\alpha\times T=\dfrac{u^2\sin2\alpha}{g}$
How do you find the speed at a given time?: $\sqrt{v_x^2+v_y^2}$ , with $v_y=u\sin\alpha-gt$ .
How do you find the direction of motion?: $\tan\phi=\dfrac{|v_y|}{|v_x|}$ and the sign of $v_y$ gives up or down.
Which root of a quadratic in $t$ do you take?: The positive one, since time cannot be negative.
How can you find the time to hit the ground from a height?: Use $s=ut+\tfrac12at^2$ vertically with the negative displacement and solve the quadratic.
What sign convention should you state?: For example 'upwards is positive', so $a=-g$ .

Exam questions on Motion in a vertical plane and projectiles

A ball is thrown vertically upwards with speed $14\text{ m s}^{-1}$ from a point $2$ m above horizontal ground. The ball is modelled as a particle moving freely under gravity. Take $g=9.8\text{ m s}^{-2}$ .
Find the speed of the ball as it hits the ground.2 marks
A particle is projected from a point $O$ on horizontal ground with speed $28\text{ m s}^{-1}$ at an angle $\alpha$ above the horizontal, where $\sin\alpha=\frac35$ . The particle moves freely under gravity and does not hit anything before it lands. Take $g=9.8\text{ m s}^{-2}$ .
Find the horizontal distance from $O$ to the point where the particle lands.2 marks
A stone is thrown from the top of a vertical cliff, $40$ m above horizontal sea level, with speed $20\text{ m s}^{-1}$ at $30^\circ$ above the horizontal. The stone is modelled as a particle moving freely under gravity. Take $g=9.8\text{ m s}^{-2}$ .
Find the time taken for the stone to reach the sea.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).