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Two bows, A and B, are used to fire arrows X and Y respectively. The average force bow A exerts is twice that of bow B and arrow X has half the mass of arrow Y. Compare the acceleration of the arrows.Question 9 options:Arrow Y will have twice the acceleration of arrow X.Both arrows will have the same acceleration.Arrow X will have four times the acceleration of arrow Y.Arrow Y will have four times the acceleration of arrow X.

Answer :

[tex]\begin{gathered} Fa=2Fb \\ mx=\frac{my}{2} \\ Fa=mx(\alpha a),\text{ }Fb=my(\alpha b) \end{gathered}[/tex][tex]\begin{gathered} 2Fb=\frac{my}{2}(\alpha a) \\ Fb=my(\alpha b) \\ \\ \frac{my}{4}(\alpha a)=my(\alpha b) \\ \alpha a=4(\alpha b) \\ \end{gathered}[/tex]

Arrow X will have four times the acceleration of arrow Y.

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