Title: Projectiles
1Projectiles
2To see a Java Applet from the University of
Virginia website which illustrates the motion of
projectiles, click HERE. Otherwise, click to
continue.
3A golf ball is hit with a speed of 50ms-1 at an
elevation of 40o along a level course.
50
40o
4A 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
5A 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
6A 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
7A 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
8A 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
9A 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
10A 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)
11A 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
12A 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
13A 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
14A 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
15A 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
16A 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
17A 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)
18A 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)
19A 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
20A 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
21A 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
22A 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)
23A 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
24A 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)
25Find 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
26Find the time of the flight
(1)
(2)
(3)
(4)
Find t when y -52 by substituting in (2)
? t 4 seconds
27Find 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
28Find 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