A particle is projected from a horizontal plane (x-y plane) such that its velocity vector at time $t$ is given by $\to V = a^i + (b - c t)^j$ . Its range on the horizontal plane is given by

\frac{b a}{c}

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\frac{2 a b}{c}

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\frac{3 b a}{c}

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\frac{b a}{2 c}

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Solution

The correct option is B $\frac{2 a b}{c}$
Given, the velocity of projection as
$\to V = a^i + (b - c t)^j$ .......(i)
Or, $\to V = V_{x}^i + V_{y}^j$
And we know that $V_{x} = u_{x}$ and $V_{y} = u_{y} - g t$
$\Rightarrow V = u_{x}^i + (u_{y} - g t)^j$ ......(ii)
Comparing (i) & (ii) we have
$u_{x} = a$ , $u_{y} = b$ and $g = c$
$∴$ Range is given by, $R = \frac{2 u_{x} u_{y}}{g} = \frac{2 a b}{c}$

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A particle is projected from a horizontal plane (x-y plane) such that its velocity vector at time t is given by →V=a^i+(b−ct)^j. Its range on the horizontal plane is given by

The correct option is B 2abcGiven, the velocity of projection as →V=a^i+(b−ct)^j.......(i) Or, →V=Vx^i+Vy^j And we know that Vx=ux and Vy=uy−gt ⇒ V=ux^i+(uy−gt)^j......(ii) Comparing (i) & (ii) we have ux=a, uy=b and g=c ∴ Range is given by, R=2uxuyg=2abc

A particle is projected from a horizontal plane (x-y plane) such that its velocity vector at time $t$ is given by $\to V = a^i + (b - c t)^j$ . Its range on the horizontal plane is given by