A body of mass $2 \,kg$ has an initial velocity of $3\, meters$ per second along $OE$ and it is subjected to a force of $4 \,N$ in a direction perpendicular to $OE$. The distance of the body from $O$ after $4$ seconds will be ........... $m$
A body of mass $2 \,kg$ has an initial velocity of $3\, meters$ per second along $OE$ and it is subjected to a force of $4 \,N$ in a direction perpendicular to $OE$. The distance of the body from $O$ after $4$ seconds will be ........... $m$
$12$
$20$
$8$
$48$
A body of mass $2 \,kg$ has an initial velocity of $3\, meters$ per second along $OE$ and it is subjected to a force of $4 \,N$ in a direction perpendicular to $OE$. The distance of the body from $O$ after $4$ seconds will be ........... $m$
Displacement of body in $4 \,sec$ along $OE$
${s_x} = {v_x}t = 3 \times 4 = 12\;m$
Force along $OF$ (perpendicular to $OE$) $= 4\, N$
$\therefore {a_y} = \frac{F}{m} = \frac{4}{2} = 2\;m/{s^2}$
Displacement of body in $4\, sec$ along $OF$
$⇒$ ${s_y} = {u_y}t + \frac{1}{2}{a_y}{t^2}$$ = \frac{1}{2} \times 2 \times {(4)^2} = 16\;m$ [As ${u_y} = 0$]
$\therefore $ Net displacement $s = \sqrt {s_x^2 + s_y^2} \; = \sqrt {{{(12)}^2} + {{(16)}^2}} = 20\;m$
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