The height of the roof is <u>3.57m</u>
Let the drops fall at a rate of 1 drop per t seconds. The first drop takes 5t seconds to reach the ground. The second drop takes 4t seconds to reach the bottom of the 1.00 m window, while the 3rd drop takes 3t s to reach the top of the window.
Calculate the distances traveled by the second and the third drops s₂ and s₃, which start from rest from the roof of the building.

The length of the window s is given by,

The first drop is at the bottom and it takes 5t seconds to reach down.
The height of the roof h is the distance traveled by the first drop and is given by,

the height of the roof is 3.57 m
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Answer:
Vi = 94.64 m/s
Explanation:
I order to find out the initial velocity of the object, we can use third equation of motion:
2ah = Vf² - Vi²
where,
a = acceleration = -9.8 m/s²
h = maximum height covered by object = 460 m - 3 m = 457 m
Vf = Final Velocity = 0 m/s (since, object momentarily stops at highest point)
Vi = Initial Velocity = ?
Therefore,
2(-9.8 m/s²)(457 m) = (0 m/s)² - Vi²
Vi = √8957.2 m²/s²
<u>Vi = 94.64 m/s</u>