1. Linear Accelerated Motion Part 2
For the Higher Level Leaving Cert Course
©Edward Williamson, Applied Maths Local Facilitator, Coachford College, Co Cork

2. Section 3 Vertical Motion

3. Gravity
Signs are always how you start e.g. if you start throwing upwards, then up is + Acceleration is g and always down. Sign depends on if you say up is + or down is +. Watch for displacement e.g. throwing something off a cliff 30 m above ground, hence displacement is -30

4. Example 3.1 [LC:1988 Q1 (b)]
A particle falls freely from rest from a point o, passing three points a, b and c, the distances ab and bc being equal. If the particle takes 3 s to pass from a to b and 2 s from b to c, calculate |ab|

5. Always go from A as initial velocity remains same+ A
u=u x
A to C
A to B B 2x
u=u, a=g, s=x, t=3
u=u, a=g, s=2x, t=5 C
Down is positive
hence g is
positive here
Solve to give x =147 m

6. Example 3.2 [LC:2002 Q1(a)]
A stone is thrown vertically upwards under gravity with a speed of u m/s from a point 30 m above the horizontal ground. The stone hits the ground 5 s later.
Find the value of u
Find the speed with which it hits the ground.

7. Displacement is -30 because up is positive
u=+u
a=-g
s=-30
t=5 +
-30
Finding v
Finding u

8. Example 3.3 [LC:1990 Q1(a)]
A particle is projected vertically upwards with velocity u m/s and is at a height h after t1 and t2 seconds respectively. Prove that:

9. u=+u
a=-g
s=+h
t=t (t1 on way up, t2 on way down) h
Solving +
Product of 2 roots
Remember α and β

10. Example 3.4 [LC:1992 Q1(a)]
A balloon ascends vertically at uniform speed. 7.2 seconds after it leaves the ground, a particle is let fall from the balloon. The particle takes 9 seconds to reach the ground. Calculate the height from which the particle was dropped.

11. Balloon + u h
For the Particle
u= +u
a= -9.8
t= 9
s= -h

12. Example 3.5 [LC:2007 Q1(a)]

13. Equations always give zero to n time
3rd second is between t=2 seconds and t=3 seconds
Equations always give zero to n time
Let x = distance travelled in first 3 seconds
Let y = distance travelled in first 2 seconds
From the Question

14. Finding Height of the tower

15. Now try some questions by yourself on the attached sheet