Shoot the Monkey! Shoot the Monkey!

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Shoot the Monkey! Shoot the Monkey!




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Presentations text content in Shoot the Monkey! Shoot the Monkey!

Slide1

Shoot the Monkey!

Slide2

Shoot the Monkey!

A monkey is sitting in a tree. For some reason you want to shoot it. But it is an astute (cheeky, even) monkey and will let go of the branch he is swinging from at the same instant you shoot your gun or arrow or blowpipe or whatever weapon you use.

So, where should you aim to guarantee hitting the blighter?

Ignoring air resistance, etc.

Slide3

Will the hunter hit his prey?

Slide4

 

 

 

 

Monkey’s initial position

Monkey’s position after time

seconds, falling under gravity,

m/s

2

 

Path of projectile

Slide5

Projectile

Monkey

After time,

Vertical displacement:

Horizontal displacement:

Time for projectile to reach fall-line of monkey

Vertical displacement

at

:

Projectile

Monkey

Vertical displacement:

Horizontal displacement:

Time for projectile to reach fall-line of monkey

Equating vertical displacements

gives:

Re-arranging gives:

So, just aim at the monkey!

 

Slide6

Projectile

Monkey

After time,

Vertical displacement:

Horizontal displacement:

Time for projectile to reach fall-line of monkey

Vertical displacement

at

:

Projectile

Monkey

Vertical displacement:

Horizontal displacement:

Time for projectile to reach fall-line of monkey

Equating vertical displacements

gives:

Re-arranging gives:

So, just aim at the monkey!

 

Slide7

Monkey’s initial position

Another way of looking at it is to consider the position vectors of each object and note how they change with time.

Considering the monkey’s position vector first:

 

Slide8

Monkey’s initial position

Path of projectile

Another way of looking at it is to consider the position vectors of each object and note how they change with time.

Now considering the projectile’s position vector:

 

Slide9

Monkey’s initial position

Another way of looking at it is to consider the position vectors of each object and note how they change with time.

Considering both position vectors:

 

 

 

so collision here

Slide10

Algebraicly:

For a collision

So

Equating horizontally:

So

Equating vertically

:

So

 

Slide11

Will the hunter hit his prey?

Slide12

HA, YOU MISSED ME!

Will the hunter hit his prey?

Slide13

Will the hunter hit his prey?

Slide14

Will the hunter hit his prey?

AAAARGHHHH!

Slide15

Will the hunter hit his prey?

First scenario – with line of fire

Slide16

Will the hunter hit his prey?

Second scenario – with line of fire

Slide17

This scenario hits the target

(line of fire is on the target)

This scenario does not hit the target

(line of fire is not on the target)

Slide18

No matter what initial velocity the projectile has the only criteria for hitting the target is that the projectile is aimed directly at it.

The initial velocity only determines

when

the target is hit. A small velocity will obviously take longer and so hunter and target should be on opposite sides of a very deep canyon!

Slide19

Another way of thinking about it is to note that each object (projectile and monkey) have identical vertical acceleration – gravity. So, subtract that motion from each object and analyse. It is now as though gravity is zero so the answer of aiming directly at the target becomes obvious.

Each object has “fallen” the same distance.

Slide20

Slide21

RESOURCES

Slide22

Will the hunter hit his prey?

Slide23

Slide24

Shoot the Monkey!

26.5 m

33.92 m

21.5 ms

-1

 

The instant you shoot, the monkey lets go and falls to the ground.

What angle ensures you hit him?

9.81 ms

-2

(Not to scale)

SIC_26

Slide25

Shoot the Monkey!

27.5 m

35.2 m

23.5 ms

-1

 

The instant you shoot, the monkey lets go and falls to the ground.

What angle ensures you hit him?

9.81 ms

-2

(Not to scale)

SIC_26

Slide26

Shoot the Monkey!

28.5 m

36.48 m

25 ms

-1

 

The instant you shoot, the monkey lets go and falls to the ground.

What angle ensures you hit him?

9.81 ms

-2

(Not to scale)

SIC_26

Slide27

Shoot the Monkey!

29.5 m

37.76 m

26.2 ms

-1

 

The instant you shoot, the monkey lets go and falls to the ground.

What angle ensures you hit him?

9.81 ms

-2

(Not to scale)

SIC_26

Slide28

Shoot the Monkey!

32.5 m

41.6 m

26.2 ms

-1

 

The instant you shoot, the monkey lets go and falls to the ground.

What angle ensures you hit him?

9.81 ms

-2

(Not to scale)

SIC_26

Slide29

Shoot the Monkey!

37.5 m

48.0 m

30 ms

-1

 

The instant you shoot, the monkey lets go and falls to the ground.

What angle ensures you hit him?

9.81 ms

-2

(Not to scale)

SIC_26

Slide30

Shoot the Monkey!

38.5 m

49.2 m

31.2 ms

-1

 

The instant you shoot, the monkey lets go and falls to the ground.

What angle ensures you hit him?

9.81 ms

-2

(Not to scale)

SIC_26

Slide31

Shoot the Monkey!

39.5 m

50.56 m

32.2 ms

-1

 

The instant you shoot, the monkey lets go and falls to the ground.

What angle ensures you hit him?

9.81 ms

-2

(Not to scale)

SIC_26

Slide32

Shoot the Monkey!

40.5 m

51.84 m

33.4 ms

-1

 

The instant you shoot, the monkey lets go and falls to the ground.

What angle ensures you hit him?

9.81 ms

-2

(Not to scale)

SIC_26

Slide33

Shoot the Monkey!

41.5 m

53.12 m

35.4 ms

-1

 

The instant you shoot, the monkey lets go and falls to the ground.

What angle ensures you hit him?

9.81 ms

-2

(Not to scale)

SIC_26

Slide34

Shoot the Monkey!

42.5 m

54.4 m

36 ms

-1

 

The instant you shoot, the monkey lets go and falls to the ground.

What angle ensures you hit him?

9.81 ms

-2

(Not to scale)

SIC_26

Slide35

Shoot the Monkey!

43.5 m

55.68 m

39.7 ms

-1

 

The instant you shoot, the monkey lets go and falls to the ground.

What angle ensures you hit him?

9.81 ms

-2

(Not to scale)

SIC_26

Slide36

Slide37


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