Using suvat with Projectiles (Edexcel A Level Maths): Revision Note
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Using suvat
How do I use the suvat equations to solve projectile problems?
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For projectile motion with acceleration a m s-2 and initial velocity u m s-1
ax = 0, ay = ±g (depending on which direction is positive)
ux = U cosθ, uy = U sinθ
Acceleration is constant so the suvat equations apply
Projectile motion is 2D so s, u, v and a are vectors
1D suvat formulae can be applied to the directions separately
(Note the formula v2 = u2 + 2as still applies in 1D)
Remember that acceleration is different for each direction
ax = 0 so the suvat formulae reduce to horizontally
How do I solve problems involving the maximum height?
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Projectile motion follows a symmetrical curve (a parabola)
Therefore there will be a maximum height that the projectile reaches
At the maximum height
Horizontal velocity, vx m s-1, will be the same as the initial horizontal velocity ux
Vertical velocity, vy m s-1 will be instantaneously zero
If the projectile launches and lands at the same height then the horizontal distance to the maximum height is half of the range of the projectile
Time t is the parameter that will be the same for both the horizontal and vertical components
Harder concepts with projectiles
You will need all your skills from your previous work with suvat
Speed is the magnitude of velocity and can be found by using Pythagoras’ Theorem
A good understanding of the relationship between distance and displacement
Simultaneous equations
Finding the point of intersection of two projectiles
Sometimes the launch and landing points will be at different heights such as if a stone is thrown from the top of a cliff into the sea
Think carefully about the vertical displacement from the start to the end
You might get asked to use the model of a projectile to decide whether an object passes over a certain height
Find the time taken to travel the horizontal distance and use this to find the maximum vertical height of the projectile
Worked Example
A stone is thrown from the top of a building which is 8 m tall. The stone is projected with speed 7 m s-1 at an angle of 600 to the horizontal. The stone is modelled as a particle and air resistance is ignored.
(a) Find the maximum height above the ground that the stone reaches.
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(b) Find the time taken for the stone to hit the ground.
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(c) Find the horizontal distance from the building to the point where the stone lands.
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Examiner Tips and Tricks
Always draw a diagram and add to it as you work through the question. Make it clear which direction you are using as positive.
Questions could ask you to find the speed at an instant, to do this remember to first find both components of the velocity and then find the magnitude of the velocity.
Not all projectiles are projected upwards, for example a cannonball fired from the turret of a castle aimed at an enemy on the ground!
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