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Standard XII

Physics

The Equation for the Path of Projectile

A particle mo...

Question

A particle moves in the plane the plane xy with velocity V = $k_{1}$ i + $k_{2}$ $\times$ j, where and j are the unit vectors of the x and y axes, and $k_{1}$ and $k_{2}$ are constants. At the initial moment of time the particle was located at the point x = y = 0 then the equation of the particle's trajectory y (x) is -

y =

\frac{k_{1}}{2 k_{2}}

x^{2}

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y =

\frac{k_{2}}{2 k_{1}}

x^{2}

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y =

\frac{2 k_{1}}{k_{2}}

x^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

y =

\frac{2 k_{2}}{k_{1}}

x^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct option is C y = $\frac{k_{2}}{2 k_{1}}$ $x^{2}$
Velocity vector

$V = k_{1}^i + k_{2} x^j$

$\frac{d x}{d t} = k_{1}, \frac{d y}{d t} = k_{2} x (1)$

$\int_{0}^{x} d x = k_{1} \int_{0}^{t} d t, x = k_{1} t (2)$

$d y = k_{2} x d t = k_{2} k_{1} d t$

$\int_{0}^{y} d y = k_{1} k_{2} \int_{0}^{t} t d t,$

$y = \frac{1}{2} k_{2} k_{1} t^{2}$

$y = \frac{k_{2}}{2 k_{1}} x^{2}$

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A particle moves in the plane the plane xy with velocity V = k1i + k2 ×j, where and j are the unit vectors of the x and y axes, and k1 and k2 are constants. At the initial moment of time the particle was located at the point x = y = 0 then the equation of the particle's trajectory y (x) is -

The correct option is C y = k22k1 x2Velocity vector V=k1^i+k2x^j dxdt=k1,dydt=k2x(1) ∫x0dx=k1∫t0dt,x=k1t(2) dy=k2xdt=k2k1dt ∫y0dy=k1k2∫t0tdt, y=12k2k1t2 y=k22k1x2

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