An Example

Problem 4: Now that the batter has a sense of the position and velocity of the ball, he can begin to plan his swing. If the ball only felt gravity in the z-direction and no force in the x-direction from this point on, where would it cross home plate.

The time of flight from y=40ft can be found from by subtracting the total time from the time to get to y=40ft,

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 = 1.152ft

vx40 = -5.706ft/s

z40 = 6.069ft

vz40 = -7.159ft/s

t = 0.4127s

th = 0.3307s