During a hurricane in 2008, the Westin Hotel in downtownNew Orleans suffered damage. Suppose a piece of glass dropped near the top of the hotel falling from the 300 meter building takes 6.62 s. Ignoring air resistance, what will the velocity of the piece of glass be when it strikes the ground?

77.8 m/s, downward

Explanation:

For uniform acceleration motion, the average speed is equal to half the soum of the initial velocity, Vi, and the final velocity, Vf

Average speed = (Vf + Vi) / 2

Also, by definition, the average speed is the distance divided by the time:

Average speed = distance / time

Then:

(Vf + Vi) / 2 = 300m/6.62s

Other kinematic equation for uniform acceleration is:

Vf = Vi + a*t

Since the window is falling and the air resistance is ignored, a = g (gravitational acceleration ≈ 9.8m/s²)

Replacing the known values we can set a system of two equations:

From (Vf + Vi) / 2 = 300m/6.62s

(Vf + Vi) = 2 * 300m/6.62s

Vf + Vi = 90.634 equation 1

From Vf = Vi + a*t

Vf - Vi = 9.8 (6.62)

Vf - Vi = 64.876 equation 2

Adding the two equations:

2Vf = 155.510

Vf = 77.8 m/s downward (velocities must be reported with their directions)