Lecture 6 Purdue University, Physics 220 1 Lecture 06 Projectile Motion Textbook Sections 4.2 PHYSICS 220 Lecture 6 Purdue University, Physics 220 2 Relative Velocity • We often assume that our reference frame is attached to the Earth. What happen when the reference frame is moving at a constant velocity with respect to the Earth? • The motion can be explained by including the relative velocity of the reference frame in the description of the motion. The ground velocity of an airplane is the vector sum of the air velocity and the wind velocity. Using the air as the intermediate reference frame, ground speed is: Example airplane V(PG)=V(PA) +V(AG) Lecture 6 Purdue University, Physics 220 3 Three swimmers can swim equally fast relative to the water. They have a race to see who can swim across a river in the least time. Relative to the water, Beth (B) swims perpendicular to the flow, Ann (A) swims upstream, and Carly (C) swims downstream. Which swimmer wins the race? A) Ann B) Beth C) Carly correct A B C x y Exercise ! t = d / v y Ann v y = v cos(!) Beth v y = v Carly v y = v cos(!) Lecture 6 Purdue University, Physics 220 4 What angle should Ann take to get directly to the other side if she can swim 5 mph relative to the water, and the river is flowing at 3 mph? A B C V Ann,ground = V ann,water +V water,ground x y x-direction: sin(!) = |V water,ground |/ |V ann,water | sin(!) = 3/5 ! Exercise
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Lecture 6 Purdue University, Physics 220 1
Lecture 06
Projectile Motion
Textbook Sections 4.2
PHYSICS 220
Lecture 6 Purdue University, Physics 220 2
Relative Velocity
• We often assume that our reference frame is attached to the Earth. What
happen when the reference frame is moving at a constant velocity with
respect to the Earth?
• The motion can be explained by including the relative velocity of the
reference frame in the description of the motion.
The ground velocity of an
airplane is the vector sum of
the air velocity and the wind
velocity. Using the air as the
intermediate reference frame,
ground speed is:
Example airplane
V(PG)=V(PA) +V(AG)
Lecture 6 Purdue University, Physics 220 3
Three swimmers can swim equally fast relative to the water. Theyhave a race to see who can swim across a river in the least time.Relative to the water, Beth (B) swims perpendicular to the flow, Ann(A) swims upstream, and Carly (C) swims downstream. Whichswimmer wins the race?
A place-kicker kicks a football at an angle of !=400
above the horizontal axis. The initial speed of the
ball is v0=22 m/s. Ignore air resistance and find the
range R that the ball attains.
v0=22m/s
!=400
H
R
The Range of a Kickoff
Lecture 6 Purdue University, Physics 220 13
y = y0 + v0yt - 1/2 gt2
vy = v0y - gt
vy2 = v0y
2 - 2g "y
x = x0 + v0xt
vx = v0x
• Use the equations
v0x = v0cos ! =
(22m/s)cos 400 = 17 m/s v0x!
v0yv0
The Range of a Kickoff
• The range is a characteristic of the horizontal motion
• You need v0x and v0y but you have been given v0
Lecture 6 Purdue University, Physics 220 14
The Range of a Kickoff
v0x!
v0yv0
v0y =v0sin !=
(22m/s)sin 400=14 m/s
• We could be done if we know the time of flight of the kickoff
• The time of flight can be determined from y equations. For
example the time to get to height H is
• Therefore the time to determine the range is #2.9 s
x = R = v
0xt
vy= v
0 y! gt
th=
v0 y! v
y
g=
14m / s
9.8m / s2= 1.428s
x = R = v
0xt = (17m / s)(2.9s) = 49m
• The range depends on the angle ! at which the football is kicked.
Maximum range is reached for !=450
Lecture 6 Purdue University, Physics 220 15
Range of a Projectile Demo 1D-22
•Two ways to hit a target except at limit
Lecture 6 Purdue University, Physics 220 17
You are a vet trying to shoot a tranquilizer dart into a monkey hangingfrom a branch in a distant tree. You know that the monkey is verynervous, and will let go of the branch and start to fall as soon as your gungoes off. On the other hand, you also know that the dart will not travel ina straight line, but rather in a parabolic path like any other projectile. Inorder to hit the monkey with the dart, where should you point the gunbefore shooting?