Kinematics balloon problem help

[Mitchtwitchita]

Homework Statement

A student at a window on the second floor of a dorm sees his physics professor coming along the walkway beside the building. He drops a water balloon from 18.0 m above the ground when the prof is 1.00 m from the point directly beneath the window. If the prof is 180 cm tall and walks at a rate of 0.450 m/s, does the balloon hit his head?

The Attempt at a Solution

Yo = 0
y = -18.0 m + 1.8 m = -16.2 m
g = -9.81 m/s^2
Vo = 0
X = 1.00 m
Vxo = 0.450 m/s

Balloon Drop:

y = yo + Vo*t - 1/2*g*t^2
-16.2 m = 0 + 0 - 1/2(9.81 m/s^2)t^2
t^2 = 16.2 m/4.9 m/s^2
t^2 = 3.31 s^2
therefore, t = sqrt3.31 s^2
= 1.82 s

Professor Walk:

x = Vxo*t
1.00 m = (0.450 m/s)t
t = 1.00 m/(0.450 m/s)
=2.22 s

Therefore, the balloon drops before the professor gets there.

Can anybody please tell me if my attempt is o.k.?

 

[Kurdt]

Looks fine to me.

 

[Mitchtwitchita]

Thanks Kurdt!