Problem

(II) An 88-g arrow is fired from a bow whose string exerts an average force of 110 N on...

(II) An 88-g arrow is fired from a bow whose string exerts an average force of 110 N on the arrow over a distance of 78 cm. What is the speed of the arrow as it leaves the bow?

Step-by-Step Solution

Solution 1

Mass of arrow \((\mathrm{m})=0.088 \mathrm{~kg}\)

Force exerted by string \((F)=110 N\)

Distance through which force acts \((d)=0.78 \mathrm{~m}\)

Work done on arrow \(=\) change in K.E

\(W=1 / 2 m\left(v^{2}-v_{0}^{2}\right)\) Where

\(v=\) Final velocity of arrow

\(v_{0}=\) Initial velocity of arrow

\(W=1 / 2 m\left(v^{2}-0\right)\)

But the Work done \(\mathrm{W}=\mathrm{Fd} \cos 0^{\circ}\)

Or \(F \cdot d=1 / 2 \mathrm{mv}^{2}\)

$$ \begin{aligned} &110 \times 0.78=1 / 2 \times 0.088 \times v^{2} \\ &v^{2}=\frac{110 \times 0.78 \times 2}{0.088} \\ &v=44 \mathrm{~m} / \mathrm{s} \end{aligned} $$

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