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# Projectile Motion - PowerPoint PPT Presentation

Projectile Motion. YouTube - Baxter NOOOOOOOOOO. Amazing facts!. If a gun is fired horizontally, and at the same time a bullet is dropped from the same height. They both hit the ground at the same time. Amazing facts!. Amazing facts!. Amazing facts!. Amazing facts!.

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Presentation Transcript

If a gun is fired horizontally, and at the same time a bullet is dropped from the same height. They both hit the ground at the same time.

Mr Porter can demonstrate this for you.

Why?

Their vertical motion can be considered separate from their horizontal motion.

Vertically, they both have zero initial velocity and accelerate downwards at 9.8 m.s-2. The time to fall the same vertical distance is therefore the same.

Imagine a dog being kicked horizontally off the top of a cliff (with an initial velocity vh).

vh

Assuming that there is negligible air resistance, he falls in the path of a parabola.

Why?

We can consider his motion to be the sum of his horizontal motion and vertical motion.

We can treat these separately

vh

Horizontal motion

Assuming no air resistance, there are no horizontal forces.

This means horizontally

the dog moves with

constant speed vh

vh

Horizontal distance travelled (x) = vht

Vertical motion

Assuming no air resistance, there is constant force downwards (=mg).

This means vertically the

dog moves with constant

acceleration g = 9.8 m.s-2

Vertical distance travelled (y) = uvt + ½gt2

Parabolic motion

Since y = ½gt2 (if u = 0) and x = vht,

y = ½gx2/vh2which you may (!) recognise as the formula of a parabola.

Another piece of ultra cool physics!

A dog is kicked off the top of a cliff with an initial horizontal velocity of 5 m.s-1. If the cliff is 30 m high, how far from the cliff bottom will the dog hit the ground?

5 m.s-1

30 m

Looking at vertical motion first:

u = 0, a = 9.8 m.s-2, s = 30 m,t = ?

s = ut + ½at2

30 = ½ x 9.8 x t2

t2 = 6.1

t = 2.47 s

The dog hits the ground after 2.47 seconds (yes!)

5 m.s-1

30 m

Now look at horizontal motion:

Constant speed (horizontally) = 5 m.s-1

Time of fall = 2.47 seconds

Horizontal distance travelled = speed x time

Horizontal distance travelled = 5 x 2.47

= 12.4 mThe dog hits the ground 12.4 metres from the base of the cliff

5 m.s-1

30 m

12.4 metres

To answer this it is easier to think in terms of the dog’s total energy (kinetic and potential)

5 m.s-1

30 m

Total energy at top = ½mv2 + mgh

Total energy = ½m(5)2 + mx9.8x30

Total energy = 12.5m + 294m = 306.5m

5 m.s-1

30 m

At the bottom, all the potential energy has been converted to kinetic energy. All the dog’s energy is now kinetic.

energy = ½mv2

V = ?

energy at top = energy at bottom

306.5m = ½mv2

306.5 = ½v2

613 = v2

V = 24.8 m.s-1

(Note that this is the dog’s

speed as it hits the ground,

not its velocity.

v = 24.8 m.s-1

Page 139 Questions 1, 2, 3 and 4.

Woof! (help)

25 m.s-1

30°

• Split the initial velocity into vertical and horizontal components

vh = 25cos30°

vv = 25sin30°

25 m.s-1

30°

2. Looking at the vertical motion, when the dog hits the floor, displacement = 0

Initial vertical velocity = vv = 25sin30°

Acceleration = - 9.8 m.s-2

25 m.s-1

30°

3. Using s = ut + ½at2

0 = 25sin30°t + ½(-9.8)t2

0 =12.5t - 4.75t2

0 = 12.5 – 4.75t

4.75t = 12.5

t = 12.5/4.75 = 2.63 s

25 m.s-1

30°

4. Looking at horizontal motion

Ball in flight for t = 2.63 s travelling with constant horizontal speed of

vh = 25cos30° = 21.7 m.s-1.

Distance travelled = vht = 21.7x2.63 = 57.1m

30°

57.1m

5. Finding maximum height? Vertically;

v = 0, u = 25sin30°, t = 2.63/2

s = (u + v)t = 12.5x1.315 = 8.2m

2 2

30°

6. Don’t forget some problems can also be answered using energy.

30°

6. Don’t forget some problems can also be answered using energy.

As dog is fired total energy = ½m(25)2

25 m.s-1

30°

6. At the highest point,

total energy = KE + GPE =½m(25cos30°)2 + mgh

As dog is fired total energy = ½m(25)2

30°

6. So ½m(25cos30°)2 + mgh= ½m(25)2

½(21.65)2 + 9.8h= ½(25)2

234.4 + 9.8h = 312.5

9.8h = 78.1

h = 8.0 m

30°

Page 140 Questions 10, 11, 12, 19.