Projectiles 4

1
Projectiles (4)
2
A football is kicked at 30o off a 30m cliff at 10
ms-1. How far will it go?
Split Velocity
Horizontal component 10 cos 30
Vertical component 10 sin 30
30m
3
Using the Constant Acceleration Equations
s ut 1/2 at2
s 1/2 (vu) t
v u at
A football is kicked at 30o off a 30m cliff at 10
ms-1. How far will it go? First find the
time of flight (TOF)
Only need to consider vertical elements to
calculate TOF
What do I want to know? t time
What do I know? a - acceleration u - initial
velocity s - displacement
-9.8 ms-2
10 sin 30 ms-1
-30 m (the drop to sea-level)
s ut 1/2 at2
Which equation involves these 4 ?
-30 10 sin 30 t 1/2 x -9.8 x t2
-30 5t - 4.9t2
4.9t2 - 5t - 30 0
4
The Quadratic Formula
for the equation ax2bxc0
5
for the equation ax2bxc0
4.9t2 - 5t - 30 0
a coefficient of x2 b coefficient of x c
constant
4.9 -5 -30
Ill assume you can do the bit in-between
t -2.02 or 3.04 (2 dp)
How come one is negative??
6
A football is kicked at 30o off a 30m cliff at 10
ms-1. How far will it go?
t -2.02
30m
7
Using the Constant Acceleration Equations
s ut 1/2 at2
s 1/2 (vu) t
v u at
A football is kicked at 30o off a 30m cliff at 10
ms-1. How far will it go? Find the range
Only need to consider horizontal elements once
TOF is found
What do I want to know? s - displacement
What do I know? a - acceleration u - initial
velocity t time
0 ms-2 (horizontally)
10 cos 30 ms-1
3.04 sec.
s ut 1/2 at2
Which equation involves these 4 ?
s 10 cos 30 x 1.53 1/2 x 0 x t2 no
horizontal acceleration
s 8.66 x 3.04 26.3 m (1 dp)
8
Maria stands 12m from the 1m tennis net and
serves the ball horizontally at U ms-1 from
1.75m. If the ball just clips the net - how
long did it take to reach the top of the
net? how hard did she hit it? how far past the
net did it land? how loud did she grunt?
the displacement s is -0.75m (because its down)
9
Using the Constant Acceleration Equations
s ut 1/2 at2
s 1/2 (vu) t
v u at
Maria stands 12m from the 1m tennis net and
serves the ball horizontally at U ms-1 from
1.75m. Find the time to the net
Only need to consider vertical elements to
calculate TOF
What do I want to know? t time
What do I know? a - acceleration u - initial
velocity s - displacement
-9.8 ms-2
0 ms-1 (hit horizontally)
-0.75 m (the drop to the net)
s ut 1/2 at2
Which equation involves these 4 ?
-0.75 0 x t 1/2 x -9.8 x t2
-0.75 -4.9t2
t ?(0.75/4.9) 0.391 sec.
4.9t2 0.75
10
Using the Constant Acceleration Equations
s ut 1/2 at2
s 1/2 (vu) t
v u at
Maria stands 12m from the 1m tennis net and
serves the ball horizontally at U ms-1 from
1.75m. Find the speed U
Only need to consider horizontal elements once
TOF is found
What do I want to know? u - initial velocity
What do I know? a - acceleration s - displacement
t time
0 ms-2 (horizontally)
U ms-1
12 m
0.391 sec.
s ut 1/2 at2
Which equation involves these 4 ?
12 U x 0.391 1/2 x 0 x t2 no horizontal
acceleration
12 U x 0.391
U 12 / 0.391 (distance/time) 30.7 ms-1
11
Using the Constant Acceleration Equations
s ut 1/2 at2
s 1/2 (vu) t
v u at
Maria stands 12m from the 1m tennis net and
serves the ball horizontally at U ms-1 from
1.75m. How far past the net did it land ?
Only need to consider horizontal elements once
TOF is found
What do I want to know? s - displacement
What do I know? a - acceleration u - initial
velocity t time
0 ms-2 (horizontally)
Not right
30.7 ms-1
0.391 sec.
s ut 1/2 at2
Which equation involves these 4 ?
s 30.7 x 0.391 1/2 x 0 x t2 no horizontal
acceleration
s 30.7 x 0.391
U 12 / 0.391 (distance/time) 30.7 ms-1
12
Activity
s 1/2 (vu) t
v u at
s ut 1/2 at2

• Page 131 of your Mechanics 1 book and answer
• exercise C
• Q 1