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Standard XII

Physics

Uniform and Non Uniform

A particle is...

Question

A particle is projected from the ground at t = 0 so that on its way it just clears two vertical walls of equal height on the ground. If the particle passes just grazing the top of the walls at time $t = t_{1}$ and $t = t_{2}$ then calculate the height of the walls.

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Solution

The correct option is B

Time of Flight = $t_{1} + t_{2}$

Assume initial velocity = u

Angle of projection = $θ$

Now we know time of flight = $\frac{2 v s i n θ}{g} = t_{1} + t_{2}$

$\Rightarrow u s i n θ = \frac{(t_{1} + t_{2}) g}{2}$ .............(i)

Applying equation of motion in y-axis for part of motion where it reaches wall 1

$u_{y} = u s i n θ$

$s_{y} = h$

$t = t_{1}$

$a = - g$

$\Rightarrow h = u s i n θ t_{1} - \frac{1}{2} g t_{1}^{2}$ ........(ii)

Putting equation (i) in (ii) we get

$h = \frac{(t_{1} + t_{2}) g}{2} t_{1} - \frac{1}{2} g t_{1}^{2}$

$\Rightarrow h = \frac{g}{2} t_{1} [t_{1} + t_{2} - t_{1}]$

$h = \frac{1}{2} g t_{1} t_{2}$

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A particle is projected from the ground at t = 0 so that on its way it just clears two vertical walls of equal height on the ground. If the particle passes just grazing the top of the walls at time t=t1 and t=t2 then calculate the height of the walls.

A particle is projected from the ground at t = 0 so that on its way it just clears two vertical walls of equal height on the ground. If the particle passes just grazing the top of the walls at time $t = t_{1}$ and $t = t_{2}$ then calculate the height of the walls.