A projectile is launched from point A of the | vedclass

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Question

(A) The projectile is launched from point $A$. To land between points $C$ and $D$, the range $R$ of the projectile must satisfy the condition $AB + BC

Vedclass · Accepted Answer

$21.5$

Vedclass · Answer

(A) The projectile is launched from point $A$. To land between points $C$ and $D$, the range $R$ of the projectile must satisfy the condition $AB + BC \leq R \leq AB + BC + CD$.From the diagram, $AB = 8 \,m$, $BC = 12 \,m$, and $CD = 4.2 \,m$.Therefore, the minimum range $R_{min} = 8 + 12 = 20 \,m$ and the maximum range $R_{max} = 8 + 12 + 4.2 = 24.2 \,m$.The formula for the range of a projectile is $R = \frac{u^2 \sin 2	heta}{g}$.Given $	heta = 15^{\circ}$, so $2	heta = 30^{\circ}$ and $\sin 30^{\circ} = 0.5$.Substituting the values: $20 \leq \frac{u^2 	imes 0.5}{10} \leq 24.2$.$20 \leq \frac{u^2}{20} \leq 24.2$.$400 \leq u^2 \leq 484$.Taking the square root, we get $20 \,m/s \leq u \leq 22 \,m/s$.Among the given options, $21.5 \,m/s$ lies within this range. Thus, option $A$ is the correct choice.

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