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Fbp01 Ball falling from top of building

A ball falls from the top of a 30-m tall building.

How long does it take to reach the ground?

What is the velocity of the ball on reaching the ground?

The first decision is where to place the origin of the coordinate system and orient the directions. The most convenient origin is at the top of the building. Make x positive down. This choice makes displacement, velocity and position positive.

[Note that placing the origin of the coordinate system on the ground and making the displacement positive up complicates the problem by making the ball start at + 30 m and move in the negative direction. The velocity and acceleration are also negative. If you want to make this problem confusing, this is the way to do it.]

To find the time use equation (1).

To find the velocity use equation (2).

A safer calculation of velocity is from equation (4).

The reason this is a safer calculation is that it uses original information. If you made a mistake in calculating t and used this incorrect number in equation (2) then this calculation of the velocity would be incorrect. Using an equation that requires original information is the safer way to proceed.