An object falls freely from a height of 25m onto the roof of a building 5m high. Calculate the velocity with which the object strikes the roof (g = 10ms−1).

The object falls freely, so its initial velocity is $u = 0 \text{ m/s}$.
The total height from which the object starts is $25 \text{ m}$.
The height of the roof is $5 \text{ m}$.
The acceleration due to gravity is $g = 10 \text{ m/s}^2$.
We need to find the final velocity $v$ when the object strikes the roof.

The object falls from a height of $25 \text{ m}$ to a height of $5 \text{ m}$.
The displacement $s$ is the distance fallen:

Since we have initial velocity ($u$), acceleration ($a=g$), displacement ($s$), and we need to find the final velocity ($v$), we use the equation:

Substitute the known values:

The velocity with which the object strikes the roof is $\text{20.0 m/s}$.