Question

a plane mirror is inclined at angle 30° with the horizontal surface a particle P is projected with velocity V =10m/s time when the image will come at momentarily at rest with respect to the particle
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Answer 1

Answer:

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Explanation:

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Answer 2

1.875 seconds

Explanation:

As shown in figure if we take x axis parallel to the mirror and y axis, perpendicular to the mirror

Then, the velocity v can be resolved as shown

Therefore, the velocity of the particle can be written as

$\vec V_p=V\cos30^\circ \hat i+V\sin 30^\circ \hat j$

$\implies \vec V_p=10\times\frac{\sqrt{3}}{2}\hat i+10\times\frac{1}{2}\hat j$

$\implies \vec V_p=5\sqrt{3}\hat i+5\hat j$

The velocity of the image in the mirror

The component parallel to the mirror will have the same velocity as the velocity of particle in x direction

The component perpendicular to the mirror will have the magnitude same as the component in y direction but the direction will be opposite

Therefore, the velocity of the image will be

$\vec V_i=5\sqrt{3}\hat i-5\hat j$

Velocity of image w.r.t. the particle

$\vec V_{i/p}=\vec V_p-\vec V_i$

$\implies \vec V_{i/p}=5\sqrt{3}\hat i+5\hat j-(5\sqrt{3}\hat i-5\hat j)$

$\implies \vec V_{i/p}=10\hat j$

The image will come momentarily at rest when the y component of the velocity becomes zero

This will be equal to the time period of the projectile-2

This time period is

$T=\frac{5^2\sin^2 60^\circ}{2g}$

$\implies T=\frac{5\times 5\times 3}{4\times 10}$

$\implies T=\frac{15}{8}$

$\implies T=1.875$ seconds

Hope this answer is helpful.

Know More:

Q: An object is moving toward a plane mirror with a speed 5m/sec and at the same time the mirror moves towards the object with a speed 10m/sec.calculate the velocity of the image which approaches towards the mirror.

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