Acceleration Due to Gravity - Trapdoor Timer Method

What is the relationship between the drop height of the ball bearing and the time to reach the trapdoor below ?

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When the switch is flicked the ball bearing is released from the electromagnet and the timer simultaneously starts.

When the ball bearing reaches the trapdoor below the timer stops.

Investigate displacements in the range 0.2 ≤ s ≤ 2 m