Projectiles

1
Projectiles
2
To see a Java Applet from the University of
Virginia website which illustrates the motion of
projectiles, click HERE. Otherwise, click to
continue.
3
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
40o
4
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
Write down the vector equations for the position
and velocity at time t seconds after the ball is
hit. Take g to be -10ms-2.
What are the horizontal and vertical components
of acceleration?
40o
The horizontal component is zero
The vertical component is 10.
s ut ½at2
5
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
What are the horizontal and vertical components
of acceleration?
40o
The horizontal component is zero
The vertical component is 10.
s ut ½at2
6
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
What are the horizontal and vertical components
of acceleration?
40o
The horizontal component is zero
The vertical component is 10.
s ut ½at2
7
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
What are the horizontal and vertical components
of acceleration?
40o
The horizontal component is zero
The vertical component is 10.
s ut ½at2
8
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
What are the horizontal and vertical components
of acceleration?
40o
The horizontal component is zero
The vertical component is 10.
s ut ½at2
9
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
What are the horizontal and vertical components
of acceleration?
40o
The horizontal component is zero
The vertical component is 10.
s ut ½at2
10
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
What are the horizontal and vertical components
of acceleration?
40o
The horizontal component is zero
The vertical component is 10.
(1)
s ut ½at2
(2)
11
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
What are the horizontal and vertical components
of acceleration?
40o
The horizontal component is zero
The vertical component is 10.
(1)
s ut ½at2
(2)
v u at
12
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
What are the horizontal and vertical components
of acceleration?
40o
The horizontal component is zero
The vertical component is 10.
(1)
s ut ½at2
(2)
v u at
13
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
What are the horizontal and vertical components
of acceleration?
40o
The horizontal component is zero
The vertical component is 10.
(1)
s ut ½at2
(2)
v u at
14
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
What are the horizontal and vertical components
of acceleration?
40o
The horizontal component is zero
The vertical component is 10.
(1)
s ut ½at2
(2)
v u at
15
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
What are the horizontal and vertical components
of acceleration?
40o
The horizontal component is zero
The vertical component is 10.
(1)
s ut ½at2
(2)
v u at
16
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
What are the horizontal and vertical components
of acceleration?
40o
The horizontal component is zero
The vertical component is 10.
(1)
s ut ½at2
(2)
v u at
17
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
What are the horizontal and vertical components
of acceleration?
40o
The horizontal component is zero
The vertical component is 10.
(1)
s ut ½at2
(2)
(3)
v u at
(4)
18
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
Find the greatest height reached
50
40o
At max. height H, vy 0
Use equation (4)
19
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
Find the greatest height reached
50
40o
At max. height H, vy 0
20
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
40o
At max. height H, vy 0
21
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
40o
At max. height H, vy 0
22
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
40o
At max. height H, vy 0
Now use equation (2)
23
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
Find time taken to reach the ground
50
40o
In this particular case, using the symmetrical
properties of the parabola, t 2 ?3.21 6.42
secs
24
A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
Find the horizontal distance from the start to
the landing point
50
40o
6.42 secs
The horizontal distance, or range is R x. Use
(1)
25
Find the speed and angle of elevation of the ball
at the start
(1)
(2)
(3)
(4)
Use (3) and (4) with t 0
Speed 25ms-1
Speed
If the angle of elevation is ?, then
26
Find the time of the flight
(1)
(2)
(3)
(4)
Find t when y -52 by substituting in (2)
? t 4 seconds
27
Find the distance from the foot of the cliff to
the point where the ball lands
(1)
(2)
(3)
(4)
We have already found that the duration of the
fight was 4 seconds, so substitute t 4 into (1)
x 24(4) 96 m
28
Find the velocity when the ball lands and hence
the speed and angle of entry
(1)
(2)
(3)
(4)
Substitute t 4 into (3) and (4)
Speed 40.8 ms-1
Speed
If the angle of elevation is ?, then