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Velocity of Image With Respect To Ground: Given

The document outlines the calculation of the velocity of an image with respect to the ground using the velocities of an object and a mirror. It details the steps to compute the image velocity with respect to the mirror and then combines it with the mirror's velocity to find the final image velocity. The final result is V⃗IG = −3î + 2k̂.

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akushai094
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25 views1 page

Velocity of Image With Respect To Ground: Given

The document outlines the calculation of the velocity of an image with respect to the ground using the velocities of an object and a mirror. It details the steps to compute the image velocity with respect to the mirror and then combines it with the mirror's velocity to find the final image velocity. The final result is V⃗IG = −3î + 2k̂.

Uploaded by

akushai094
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Velocity of Image with Respect to Ground

Given:
• Velocity of object with respect to mirror:
V⃗OM = −î + 2ĵ + k̂
• Velocity of mirror with respect to ground:
V⃗M G = î + ĵ + k̂
• Normal vector of the mirror:
−î − ĵ
⃗n = −î − ĵ ⇒ n̂ = √
2

Step 1: Image velocity w.r.t mirror


For a plane mirror, the velocity of the image with respect to the mirror is given by:
V⃗IM = V⃗OM − 2(V⃗OM · n̂)n̂
Compute the dot product:
!
−î − ĵ −1 − 2 −3
V⃗OM · n̂ = (−î + 2ĵ + k̂) · √ = √ =√
2 2 2
Now compute:
!
−3 −î − ĵ
V⃗IM = (−î + 2ĵ + k̂) − 2 · √ · √ = (−î + 2ĵ + k̂) − 3(î + ĵ)
2 2

⇒ V⃗IM = −4î − ĵ + k̂

Step 2: Image velocity w.r.t ground


V⃗IG = V⃗IM + V⃗M G = (−4î − ĵ + k̂) + (î + ĵ + k̂) = −3î + 2k̂

Final Answer:
V⃗IG = −3î + 2k̂

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