Measuring \( g \)
The figure shows a method for measuring the acceleration
\( \mathrm{P} \) due to gravity. The ball is projected upward by a "gun." The ball passes electronic "gates" 1 and 2 as it rises and W again as it falls. Each gate is connected to a separate timer. The first passage of the ball through each gate starts the corresponding timer, and the second passage through the same gate stops the timer. The time intervals \( \Delta t_{1} \) and \( \Delta t_{2} \) are thus measured. The vertical distance between the two gates is \( d \). If \( d=5 \mathrm{~m}, \Delta t_{1}=3 \mathrm{~s}, \Delta t_{2}= \) \( 2 \mathrm{~s} \), find the measured value of acceleration due to gravity (in \( \mathrm{m} \mathrm{s}^{-2} \) ).
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