Everything Science Grade 12

6.2 CHAPTER 6. MOTIONIN TWO DIMENSIONS

vf = vi+ gt (6.1)

Δx =

(vi+ vf)

2

t (6.2)

Δx = vit +

1

2

gt^2 (6.3)

v^2 f = v^2 i+ 2gΔx (6.4)

See simulation: VPnlc at http://www.everythingscience.co.za)

Example 1: Projectile motion

QUESTION

A ball is thrown upwards with an initial velocityof 10 m·s−^1.

1. Determine the maximum height reached above the thrower’s hand.


2. Determine the time it takes the ball to reachits maximum height.

SOLUTION

Step 1 : Identify what is required and what is given

We are required to determine the maximum height reached by

the ball and how long it takes to reach this height. We are given

the initial velocity vi= 10 m·s−^1 and the acceleration dueto grav-

ity g = 9,8 m·s−^2.

Step 2 : Determine how to approach the problem

Choose down as positive. We know that at themaximum height

the velocity of the ball is 0 m·s−^1. We therefore have thefollow-

ing:

• vi=−10 m· s−^1 (it is negative because we chose downwards as positive)


• vf= 0 m· s−^1


• g = +9,8 m· s−^2

Step 3 : Identify the appropriate equation to determinethe height.

We can use:

vf^2 = v^2 i+ 2gΔx

to solve for the height.

Step 4 : Substitute the values inand find the height.