Projectile Motion |

**What is the projectile motion of a body?**

- A body in projectile motion will move in two dimensions simultaneously. Bodies that are in projectile motion are resolved(divided) into two components. A vertical component(Vy) and an horizontal component(Vx). These components however are dealt with simultaneously.

Please refer to the diagram below showing projectile motion.

Projectile motion |

Formulas associated with projectile motion include:

- Vy = VsinA
- Vx = VcosA
- V = Sqrt [Vy^2 + Vx^2]
- TanA = Vy / Vx => A = Tan^-1 A (Vy / Vx)

Example calculation involving projectile motion:

- A body is projected with a velocity of 200m/s at and angle of 30 °C to the horizontal.

- Calculate the time taken to reach its maximum height.
- Calculate its velocity after 16 seconds.

Answers:

- Finding the time for maximum height.

V = 200m/s

Acceleration(a) = -10 m/s

^{2}

Vy = 0 m/s

Therefore Uy = VsinA

*[ Note: Uy represents initial velocity]*
Uy = 200 x Sin 30

Uy = 100 m/s

Vy = Uy = at

__Vy - Uy__= at

a

__0 - 100__= t

- 10

10 sec = t

Therefore Maximum Time (t) = 10 seconds

- Finding the velocity after 16 seconds.

Vx = V cos A

Vx = 200 x Cos 30

Vx = 173.2 m/s

Vy = Uy + at

Vy = 100 - 10 (16)

Vy = -60 m/s

Therefore V = √

`[Vy^2 + Vx^2]`

= √[

`(-60)^2 + (173.2)^2]`

= √

`33598`

`= 183.30 m/s`

## 6 Response to Projectile Motion and Example Calculations

Thanks for such an easy explanation!

Really clear way of explaining such a complex topic!

Nice explanation. It's important to understand this because, later, you'll move on to pendlums, springs, turbine blades, pump impellers, whirlpools, and cloud movement (unless you branch off into medicine or finance).

It is always very nice to come to this blog as it is very didactic.

Thanks for sharing with us these calculation examples. They are really useful.

A bullet is fired at such an angle such that the horizontal displacement is 3 times the maximum height reached by the bullet.The initial velocity of the bullet is 150m/s.Calculte the angle of projection.

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