PHYS16 – Lecture 8
Fox Trot by Bill Amend
Projectile Motion: Max Range and Height
September 24, 2010
Agenda
• Derive Shoot the Monkey
• Derive Max height and Range for Projectile
Motion
• Outside Demo Day
Derive Shoot the Monkey
• If shoot gun and monkey falls from height at
the same time, where do I aim gun to hit
monkey? (Answer: At monkey)
ymonkey
v0
θ
xmonkey
http://physics.ucr.edu/~wudka/Physics7/Notes_www/img149.gif
Derive Shoot the Monkey
1) Find time for bullet to go xmonkey, then solve for bullet’s y
position
x0  y0  0 x  x monkey
ax  0 a y   g
v0 y  v0sin ( ) v0 x  v0 cos( )
t  x monkey v0 cos( )

ay 2
y  y0  v0 y t  t
2
 x monkey  g  x monkey 
  

y  v0sin ( )
 v0 cos( )  2  v0 cos( ) 
2
Derive Shoot the Monkey
2) Find the monkey’s y position at the same time
y0  ymonkey
ay  g
v0 y  0 t  x monkey v0 cos( )

ay 2
y  y0  v0 y t  t
2
g  x monkey 

y  ymonkey  
2  v0 cos( ) 
2
Derive Shoot the Monkey
3) Set the two positions equal to each other and find out where
We should aim our gun…
 x monkey  g  x monkey 
  

y  v0sin ( )
 v0 cos( )  2  v0 cos( ) 
g  x monkey 

y  ymonkey  
2  v0 cos( ) 
tan( ) 
2
ymonkey
xmonkey
Aim at Monkey!!!
2
Derive max y & x for Projectile
x0  y0  0 a x  0 a y   g
v0 y  v0sin ( ) v0 x  v0 cos( ) v y ,arc top  0

y  y max
v y2  v02y  2a y ( y  y0 )
0  v02sin 2 ( )  2 gymax
ymax  v02sin 2 ( ) 2 g
θ

x  x max t  2tarc top  2v0sin ( ) g
xmax
ax 2
t
2
 0  v0 cos( )( 2v0sin ( ) g )  0
xmax  x0  v0 x t 
http://schools-wikipedia.org/images/189/18902.png
xmax
xmax  v02sin (2 ) g
Outside Demo Day
Drop Balls off of Merrill Beach
• Objective: to see which balls are the most
affected by air resistance
– Physics says that in vacuum all balls should fall
with the same acceleration and land at the same
time, neglecting air resistance
Shoot Water Rockets
• Objective: to determine the angle with air
resistance that allows for the max distance
– Physics says that without air resistance, angle that
give max distance is 45 degrees
Sling Shot
• Objective: Calculate the initial velocity of a
sling shot
– Shoot the sling shot only in x then measure where
it hit the ground and how long it took it to hit the
ground
– Initial velocity = distance/time, as long as you
neglect air resistance