In fig. 2.24, a student at a window on the second floor of a dorm sees his math professor walking on the sidewalk beside the building. he drops a water balloon from 18.0 m above the ground when the professor is 1.00 m from the point directly beneath the window. if the professor is 170 cm tall and walks at a rate of 0.450 m/s does the balloon hit her? if not, how close does it come?

How long will it take for the baloon to fall the distance between the professor and the window or more?
distance between professsor and window=18m-170cm=1800-170cm=1630cm

how long until the professor is directly under the window?
1m=0.450m/s times t
2.2222222=t
about 2 and 2/9 seconds

if the balloon can travel at least 1630cm in 2 and 2/9 seconds, then it will hit her

the distance traveld is d=(1/2)gt² where g is the accerlation due to gravity (about 9.81m/s²)
so
t=2.2222222222
d=(1/2)(9.81m/s²)(2.2222222222s)²
D=(9.81m)(2.22222222222222)(1.111111111)
D≈0.24222222222222222222222222222222m≈24.222cm

it needs to travel 1630cm
you failed
it came within 1605.77777777cm of the professor