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# Question 42

(a) How long will a stone take a fall to the ground from the top of a building 80m high and (b) what will be the velocity of the stone on reaching the ground? (Take g=10m/s^2)

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Given: height=80m, g=10m/s^2

(a)From the equation of motion;

\begin{array}{l} \mathrm{H}=\mathrm{ut}+1 / 2 \mathrm{gt}^{2} \\ \Rightarrow 80=0(\mathrm{t})+1 / 2(10) \mathrm{t}^{2} \\\Rightarrow 160=10 \mathrm{t}^{2} \\ \Rightarrow \mathrm{t}=4 \mathrm{s} \end{array}

(b) To find the velocity of the stone, assume ‘v’ to be the velocity

From the equation of motion;

\begin{array}{l} \mathbf{v}^{2}-\mathbf{u}^{2}=2 \mathrm{gh} \\ \mathbf{v}^{2}-0=2(10)(80) \\ \mathbf{v}^{2}=1600 \\ \mathbf{v}=40 \mathrm{m} / \mathrm{s} \end{array}

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