Projectile motion

1
Projectile motion

• A projectile is an object upon which the only
  force acting is gravity.
• It is assumed that the influence of air
  resistance is negligible.

2
Monkey and Hunter Experiment
3
Only one force (weight) is acting on the cannon
ball.
Horizontal motion Constant velocity
vertical motion Constant downward acceleration g
4
Horizontal motion No horizontal force gt
constant velocity
Vertical motion Downward force (weight) gt
uniform downward acceleration (g)
5
A projectile motion
Speed of projection u Angle of projection a
u
Initial horizontal speed u cos a Initial
vertical speed u sin a
u sin a
a
u cos a
Horizontal displacement x u cos a t Vertical
displacement y u sin a t ½ gt2
6
Time of flight
t 0

• Put y 0
• 0 u sin a t ½ gt2
• t(u sin a ½ gt) 0
• t 0 (rejected) or t 2u sin a / g

t time of flight
7
Range
Range final horizontal displacement
horizontal speed x time of flight
u cos a x 2u sin a / g 2 u2 sin a cos a / g
u2 sin 2 a /g
8
Maximum Range
Range 2 u2 sin a cos a / g u2 sin
2 a /g Maximum range u2 /g when sin 2 a 1
i.e. 2a 90o a 45o
9
Summary

• Vertical motion y ut sin q ½ gt2
• Horizontal motion x ut cos q
• Time of flight Put y 0
• ? t 2usin q / g
• Range Put t 2u sin q / g
• ? x u2sin 2q / g

10
Exercise (HKAL 1998) page 28

• A small object is thrown horizontally towards a
  vertical wall 1.2 m away. It hits the wall 0.8 m
  below its initial horizontal level. At what speed
  does the object hit the wall? (Neglect air
  resistance.)

wall
1.2 m
0.8 m
11
Solution
wall
1.2 m
u
0.8 m
? ut 1.2 ? u 1.2/0.4 3 ms-1 At the wall, (v
u at) Horizontal velocity 3 (0)(0.4) 3
ms-1 Vertical velocity 0 (10)(0.4) 4
ms-1 The speed at the wall (32 42)½ 5
ms-1

• Horizontal motion x ut cos q
• ? 1.2 ut cos 0o
• ? ut 1.2
• Vertical motion y ut sin q ½ gt2
• ? 0.8 ut sin 0o ½ gt2
• ? 0.8 ½ (10)t2
• ? 0.8 ½ (10)t2
• ? t 0.4 s

12
Class work page 13

• (a) Time of flight
• By s ut ½ at2
• -100 10 sin 30ot ½ (-10) t2
• 5t2 5t 100 0
• (t 5)(t 4) 0
• t 5 s or t -4 s (rejected)

13
Class work page 13

• (b) Horizontal distance moved
• u cos 30o x time of flight
• 10 cos 30o x 5
• 43.3 m

14
Class work page 13

• (c) Direction of flight
• vx 10 cos 30o 8.66 ms-1
• vy 10 sin 30o (-10)(5) -45 ms-1
• tan q vy / vx 45/8.66
• q 79.1o
• ? The particle makes an angle of 79.1o to the
  horizontal when it reaches the sea.

15
Class work page 13
vx
q
vy
v

• (d) Speed of the ball
• sqrt(vx2 vy2)
• sqrt(8.662 452)
• 45.83 ms-1

16
Homework

• Textbook page 51 (6, 7)
• Reference book page 116 (8, 12, 16)
• Due date 2nd October
• Test Chapter 4 projectile motion
• 2nd October