2.6.2 Using suvat

2-6-1-horizontal-_-vertical-components-diagram-2

For projectile motion with acceleration a m s^-2 and initial velocity u m s^-1
- a_x = 0, a_y = ±g (depending on which direction is positive)
- u_x = Ucosθ, u_y = Usinθ
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
- a_x = 0 so the suvat formulae reduce to s_x = u_xt horizontally

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, v_x m s^-1, will be the same as the initial horizontal velocity u_x
- Vertical velocity, v_y 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

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

2.6.2_WE_Using Suvat_1

(a) Find the maximum height above the ground that the stone reaches.

2-6-2-using-suvat-example-solution-aqa-a

(b) Find the time taken for the stone to hit the ground.

2-6-2-using-suvat-example-solution-aqa-b

2-6-2-using-suvat-example-solution-aqa-c

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!
Remember to round answers to 2 significant figures if g=9.8 is used.

AQA A Level Maths: Mechanics

2.6.2 Using suvat