Projectiles 2

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Projectiles (2)
2
Projectile Motion
Objects thrown in a PROJECTILE MOTION fly in a
parabola
in Mechanics 1 all projectile motion - assumes
negligible mass - assumes no air resistance -
no wind - no spin
3
This is no good. Wind and air resistance will
effect the motion too much.
4
Freddie hitting a six
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Constant Acceleration Equations in 2D
Given as vectors v - final velocity u - initial
velocity a - acceleration s - displacement As a
scaler t time
j
i
a will always be -9.8j ms-2
6
A football is kicked horizontally off a cliff at
10 ms-1
u - initial velocity ?
u 10i ms-1
What is the displacement through time?
s ut 1/2 at2
s 10i t 1/2 x -9.8j x t2
s 10t i - 4.9 t2 j
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s 10t i - 4.9 t2 j
Time 0 1 2 3 4
5 Displacement
20i -19.6j
30i -44.1j
40i -78.4j
50i -122.5j
10i -4.9j
0
Parabolic Motion
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A ball is thrown with an initial velocity of (4i
6j) ms-1 . Find the magnitude and direction of
the velocity after 1 second? How long does
it fly for? How far does it go?
Can assume parabolic motion
In projectile questions you only need to consider
the vertical element of the motion 6j ms-1 to
work out time of flight
The time calculated from above, together with the
horizontal element of the motion 4i ms-1, will
give the range (horizontal displacement)
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Using the Constant Acceleration Equations
s ut 1/2 at2
s 1/2 (vu) t
v u at
A ball is thrown with an initial velocity of (4i
6j) ms-1 . Find the magnitude and direction of
the velocity after 1 second
What do I want to know? v - velocity
What do I know? a - acceleration u - initial
velocity t time
-9.8j ms-2
(4i 6j) ms-1
1 sec.
v u at
Which equation involves these 4 ?
v (4i 6j) -9.8j x 1
v 4i 6j - 9.8j
v 4i - 3.8j ms-1
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Find the magnitude and direction of the velocity
v 4i - 3.8j ms-1
Magnitude of velocity ?(42 3.82)
?30.44 5.5 ms-1 (1dp)
tan ? opp/adj 3.8/4 ? tan-1(0.95) 43.5o
43.5o below the horizontal
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Using the Constant Acceleration Equations
s ut 1/2 at2
s 1/2 (vu) t
v u at
A ball is thrown with an initial velocity of (4i
6j) ms-1 . How long does it fly for?
What do I want to know? t time
What do I know? a - acceleration u - initial
velocity s - displacement
-9.8j ms-2
(4i 6j) ms-1
(?i 0j) m
s ut 1/2 at2
Which equation involves these 4 ?
Only need to consider vertical elements
0j 6jt 1/2 x -9.8j x t2
Either t 0 start or 6 - 4.9t 0 t
6/4.9 1.22 sec.
0 6t - 4.9t2
0 t(6 - 4.9t)
12
Using the Constant Acceleration Equations
s ut 1/2 at2
s 1/2 (vu) t
v u at
A ball is thrown with an initial velocity of (4i
6j) ms-1 . How far does it fly?
What do I want to know? s - displacement
What do I know? a - acceleration u - initial
velocity t time
-9.8j ms-2
(4i 6j) ms-1
(?i 0j) m
1.22 sec.
s ut 1/2 at2
Which equation involves these 4 ?
Only need to consider horizontal elements
s 4i x 1.22 1/2 x 0 x t2 no horizontal
acceleration
s 4i x 1.22 4.9 m (1 dp)
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Activity
s 1/2 (vu) t
v u at
s ut 1/2 at2

• Page 126 of your Mechanics 1 book and answer
• exercise B
• Q 1