PASCO ME-6800 Projectile Launcher (Short Range) - Manual (Page 47)

®
M o d e l N o . M E - 6 8 0 0 T e a c h e r ’ s G u i d e
0 1 2 - 0 5 0 4 3 G 43
• and simplify:
• When x = x
max
, the value of this derivative is negative.
• Therefore, the ball has already reached the peak and is on its way down.
2. Solve the equation for maximum angle to determine x:
• Substitute this value into the equation for y to determine the maximum height.
dy
dx
------
v
0
2
gx
max
--------------
gx
v
0
2
gx
max
v
0
4
g
2
x
max
2
+
---------------------------------
 
 
  2
----------------------------------------------- –
v
0
2
gx
max
--------------
x v
0
4
g
2
x
2
max
+
 
v
0
2
gx
max
2
--------------------------------------- – = =
dy
dx
------
v
0
gx
max
--------------
v
0
x
gx
2
max
----------------- –
gx
v
0
2
------ – =
dy
dx
------
x
max
gx
max
v
0
2
-------------- – =

max
tan
v
0
2
gx
------ x

v
0
2
g
----- = =
y y
0
v
0
2
g
-----
g
v
0
2
g
-----
 
 
 
2
v
0
2
---------------- – + y
0
v
0
2
g
-----
v
0
2
g
----- – + = =
y y
0
=