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Mechanics 2 Chapter 1 :: Projectiles

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Overview

 

“A particle is projected horizontally at 20 ms-1, at a distance 50m above the ground. How far along the ground does it travel?”

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1:: Horizontally projected

 

2:: Projection at any angle

50m

 

 

 

 

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Acceleration in each direction.

The key is separately considering the motion in the vertical and horizontal directions:

 

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[Textbook] A particle is project horizontally at 25 ms-1 from a point 78.4 metres above a horizontal surface. Find:

  1. the time taken by the particle to reach the surface
  2. the horizontal distance travelled in that time.
  3. the distance of the impact point from the original point.

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78.4m

 

 

 

Just using ‘sdt triangle’:

s

d

t

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a

b

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Further Example

 

122.5m

90 m

 

 

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Test Your Understanding

 

 

100 m

 

 

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Exercise 1A

Pearson Mechanics 2

Pages 4-6

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Components of velocity

Just as we split forces into its horizontal and vertical components, in order to consider forces in the horizontal and vertical directions respectively, we can do exactly the same with velocity!

 

 

 

 

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When the object is at its highest point:

The vertical velocity is 0.

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We know that the scalar form of velocity is speed, and thus we just find the magnitude of the velocity vector:

 

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Click for Tomanimation

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Simple Example

 

 

Vertically the particle has returned to its original position, so displacement is 0.

 

 

 

 

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a

b

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Projected from above ground

 

 

 

 

 

 

 

 

 

 

 

 

? Diagram

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(It’s important you draw one!)

 

a

b

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Time above a given point

 

 

 

Use the quadratic solver on your calculator.

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Test Your Understanding

Edexcel M2(Old) May 2012 Q7

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b

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c

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Exercise 1C

Pearson Mechanics 2

Pages 11-13

 

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Projectile Formulae

There’s nothing new here, but you may be asked to prove more general results regarding projectile motion.

 

 

 

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b

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Projectile Formulae

 

a

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Don’t be intimidated by the lack of numerical values. Just do what you’d usually do and resolve both vertically and horizontally!

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Projectile Formulae

 

b

 

 

 

This is an interesting result, because in general, for a fixed initial speed, there are 2 (and only 2) angles which result in a specified (reachable) point being passed.

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General Results

Exam Note: You may be asked to derive these. But don’t attempt to memorise them or actually use them to solve exam problems – instead use the techniques used earlier in the chapter.

 

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Exercise 1D

Pearson Mechanics 2

Pages 17-19