ProjectileProjectile : an object acted upon only : an object acted upon only by the force of gravityby the force of gravity

Putting our SUVAT equations to good usePutting our SUVAT equations to good use

Learning Objectives :Learning Objectives :

1.1. To understand the concept of To understand the concept of projectilesprojectiles

2.2. To be able to complete projectile To be able to complete projectile calculations successfullycalculations successfully

NOTE you can ignore “projectiles” NOTE you can ignore “projectiles” altogether and just consider it normal altogether and just consider it normal SUVAT workSUVAT workBook Reference : Pages 126-127Book Reference : Pages 126-127

A fun example.... A fun example.... [SoccerBall][SoccerBall]

What sort of problems do we need to solve?What sort of problems do we need to solve?

Problems with only a vertical aspectProblems with only a vertical aspect

““Releasing an object from a hot air balloon”Releasing an object from a hot air balloon”

Problems with both horizontal and vertical Problems with both horizontal and vertical aspectsaspects

““Putting a golf ball off of the top of a cliff”Putting a golf ball off of the top of a cliff”

101 possible questions about distance, speed, 101 possible questions about distance, speed, time etc etc Both horizontally and verticallytime etc etc Both horizontally and vertically

Starting points....Starting points....

1.1.We need to consider vertical &horizontal components We need to consider vertical &horizontal components of motion & they are independentof motion & they are independent

2.2.The acceleration involved is always The acceleration involved is always gg (downwards) & (downwards) & only affects the vertical componentonly affects the vertical component

3.3.Any horizontal velocity is constant and unaffected by Any horizontal velocity is constant and unaffected by gg

4.4.We’ll consider up as positive and down as negativeWe’ll consider up as positive and down as negative

Watch the following telly if you are not convinced![02_Parabolic_motion_and_uniformly_accelerated_linear_motion]

Note : Horizontally there is no change in velocity, (1 square per photo all the way across)

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Vertical Projection OnlyVertical Projection Only

1.1.As the name suggests, the object only travels verticallyAs the name suggests, the object only travels vertically

2.2.Vertical velocity at any moment is given by a variation Vertical velocity at any moment is given by a variation on our 1on our 1stst SUVAT equation SUVAT equation

v = u - gtv = u - gt

3.3.Our displacement at any moment is given by a Our displacement at any moment is given by a variation on our 3variation on our 3rdrd SUVAT equation SUVAT equation

y = ut -½gty = ut -½gt22

4.4.If there is an initial positive vertical projection If there is an initial positive vertical projection (upwards). then the vertical velocity will be zero at the (upwards). then the vertical velocity will be zero at the highest point.highest point.

5.5.Remember to use other SUVAT equations as requiredRemember to use other SUVAT equations as required

Horizontal ProjectionHorizontal Projection

1.1.It starts with a perfectly horizontal motionIt starts with a perfectly horizontal motion

2.2.As it accelerates vertically downwards its path As it accelerates vertically downwards its path becomes steeper and steeperbecomes steeper and steeper

3.3.Speed of horizontal projection affects how far Speed of horizontal projection affects how far away it landsaway it lands

4.4.But does not affect how long it stays in the airBut does not affect how long it stays in the airWe can watch the telly again if you are not convinced!

Horizontal ProjectionHorizontal Projection

If the object is projected with a horizontal velocity If the object is projected with a horizontal velocity uu then after then after tt seconds.... seconds....

Horizontal component of its displacementHorizontal component of its displacement

x = utx = ut

Vertical component of its displacementVertical component of its displacement

y = ½gty = ½gt22

There is no initial vertical componentThere is no initial vertical component

u

½gt2

ut

Displacements at time Displacements at time tt

vy

vx

√√(v(vxx2 + vvyy

2))

We can use trigonometry to find We can use trigonometry to find θ θ the direction of our the direction of our combined velocitycombined velocity

For example tan For example tan θθ = v = vyy / v / vxx

θ

A worked example....A worked example....

An object is projected at a horizontal An object is projected at a horizontal velocity of 15 msvelocity of 15 ms-1-1 from the top of a 35m from the top of a 35m tower. Calculate the followingtower. Calculate the following

a)a)How long it takes to reach the ground (2.67s)How long it takes to reach the ground (2.67s)b)b)How far it travels horizontally (40m)How far it travels horizontally (40m)c)c)It’s speed at impact (30.2 msIt’s speed at impact (30.2 ms-1-1))