The figure shows a method for measuring the acceleration due to gravity. The ball is projected upwar

Question

The figure shows a method for measuring the acceleration due to gravity. The ball is projected upward by a gun. The ball passes electronic gates 1 and 2 as it rises and 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 $\mathrm{ms}^{-2}$ ).

Professor PC Thomas Classes · Answer

(d) : $1.5=\frac{v_1}{a} ; 1=\frac{v_2}{a} ; 5=\frac{v_1^2-v_2^2}{2 a} \Rightarrow a=8$