An Example

Problem 3:Since a typical batter doesn’t get a sense of the motion of the pitch until the ball is about 40ft away from home plate, find the time to get there and the x and z components of the position and velocity when it arrives.

The x-position and velocity can now be found,

xo = 1.664ft

yo = 50.00ft

zo = 6.597ft

vxo = -6.791ft/s

vyo = -123.055ft/s

vzo = -5.721ft/s

ax = 13.233ft/s2

ay = 25.802ft/s2

az = -17.540ft/s2

t40 = 0.08197s

x40 = ?

vx40 = ?

z40 = ?

vz40 = ?

as can the z-position and velocity,

t40 = 0.08197s

x40 = 1.152ft

vx40 = -5.706ft/s

z40 = 6.069ft

vz40 = -7.159ft/s

t = 0.4127s