Physics 199BBThe Physics of Baseball

ax
vx t
dvx dt
d2y dt 2
• Acceleration is a vector with three components
r
r dv
d
2
rபைடு நூலகம்r
a = (ax ,a y ,az )= dt dt2
Week 2
5
Motion with Constant Acceleration
x = x0 + v0t + ½at2 v = v0 + at
• x = x0 + v0xt vx = vx0 (constant)
• y = y0 + v0yt - ½gt2 vy = v0y - gt
Week 2
7
Detailed example: pitched baseball
• Suppose a pitcher throws a baseball with an initial horizontal velocity of 90 mph at a height of 6 ft above home plate. How long does the pitch take to reach home plate? How much does the pitch drop vertically?
= 6 ft – 3.382 ft = 2.618 ft
Ball drops ~3.4 ft!
Week 2
11
Using Excel to Compute the Trajectory
Week 2
2
Position, Velocity, and Acceleration
1. Position: x,y,z
• Units of length (m, ft, …) • Trajectory completely known if we know the position
of an object at every instant of time x(t),y(t),z(t)
Special Case 1: a=0
x = x0 + v0t v = v0
Week 2
6
Special Case 2: Two-dimensional projectile motion
with gravity
ax = 0 (horizontal) ay = -g (vertical)
g = 32.2 ft/s2 = 9.8 m/s2
Physics 199BB The Physics of Baseball
Fall 2007 Freshman Discovery Course
Alan M. Nathan 403 Loomis 333-0965
a-nathan@
Week 2
Week 2
1
The Flight of a Baseball
• The goal: to develop an understanding of the trajectory of a baseball in flight
– Pitched baseball – Batted baseball – Thrown baseball
• First step: we need to go over some basic physics concepts
• Velocity is the rate of change of position x dx
vx t dt
• Velocity is a vector wirth three components
r
dr
v = (vx ,vy ,vz )= dt
speed = magnitude of vr =
• Position is a verctor with three components r = (x,y,z)
Week 2
3
Position, Velocity, and Acceleration
2. Velocity vx,vy,vz
• Units of length/time (m/s, ft/s,mph,…)
x = x0 + v0xt
x0=0 v0x = 90 mph
y = y0 + v0yt - ½gt2 y0=6 ft v0y=0
Week 2
8
Detailed example: pitched baseball
x = x0 + v0xt
x0=0 v0x = 90 mph
y = y0 + v0yt - ½gt2 y0=6 ft v0y=0
Want to find time T when x = 60.5 ft. Use that T to find y. But first…need a consistent set of units. Convert mph to f/s
90 mile/hour = 90 (mile/hour)(5280 ft/mile)(1/3600 hour/sec) =90*1.467=132.0 ft/s
Week 2
9
Useful thing to remember
• To convert mph to ft/s, multiply by 1.467 • To convert ft/s to mph, divide by 1.467
Week 2
10
Detailed example: pitched baseball
v
2 x
+v
2 y
+v2z
Week 2
4
Position, Velocity, and Acceleration
3. Acceleration ax,ay,az
• Units of length/time2 (m/s2, ft/s2,…)
• Acceleration is the rate of change of velocity
x = x0 + v0xt
x0=0 v0x = 90 mph
y = y0 + v0yt - ½gt2 y0=6 ft v0y=0
Now solve to find T: 60.5 ft = 0 + 132T ft/s T=0.458 s
Now solve to find y(T):
Y = 6 ft + 0 -0.5*32.2 ft/s2*(0.458)2 s2