A vector P directed along the X-axis is added | vedclass

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(D) Let vector $P = P \hat{i}$.Since vector $Q$ has a magnitude of $10 \ m$,let $Q = 10 \cos 	heta \hat{i} + 10 \sin 	heta \hat{j}$.The resultant ve

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$2 \sqrt{5} \ m$

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(D) Let vector $P = P \hat{i}$.Since vector $Q$ has a magnitude of $10 \ m$,let $Q = 10 \cos 	heta \hat{i} + 10 \sin 	heta \hat{j}$.The resultant vector $R = P + Q = (P + 10 \cos 	heta) \hat{i} + (10 \sin 	heta) \hat{j}$.Given that the resultant is directed along the $Y$-axis,the $X$-component must be zero:$P + 10 \cos 	heta = 0 \Rightarrow 10 \cos 	heta = -P$.The magnitude of the resultant is $R = 10 \sin 	heta$.We are given $R = 2P$,so $10 \sin 	heta = 2P \Rightarrow 5 \sin 	heta = P$.Using the identity $\sin^2 	heta + \cos^2 	heta = 1$:$(P/5)^2 + (-P/10)^2 = 1$.$P^2/25 + P^2/100 = 1$.$(4P^2 + P^2) / 100 = 1 \Rightarrow 5P^2 = 100$.$P^2 = 20 \Rightarrow P = \sqrt{20} = 2 \sqrt{5} \ m$.

$A$ vector $P$ directed along the $X$-axis is added to vector $Q$ which has a magnitude of $10 \ m$. The resultant vector is directed along the $Y$-axis,with a magnitude that is $2$ times that of $P$. The magnitude of $P$ is

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