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A police jeep is chasing with velocity of $45 \mathrm{~km} / \mathrm{h}$. A thief in another jeep moving with velocity $153 \mathrm{~km} / \mathrm{h}$. Police fires a bullet with muzzle velocity of $180 \mathrm{~m} / \mathrm{s}$. The velocity it will strike the car of the thief is
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The correct answer is:
$150 \mathrm{~m} / \mathrm{s}$
Effective speed of bullet is \(=\) Speed of bullet + Speed of police jeep
\(\begin{aligned}
& =18 \mathrm{om} / \mathrm{s}+45 \mathrm{~km} / \mathrm{hr} \\
& =180+45 \times \frac{5}{18} \mathrm{~m} / \mathrm{s} \\
& =192.5 \mathrm{~m} / \mathrm{s}
\end{aligned}\)
Speed of theifs jeep \(=153 \mathrm{~km} / \mathrm{hr}=42.5 \mathrm{~m} / \mathrm{s}\)
Velocity of bullet with respect to theif's jeep \(=192.5-42.5 \mathrm{~m} / \mathrm{s}\)
\(=150 \mathrm{~m} / \mathrm{s}\)
\(\begin{aligned}
& =18 \mathrm{om} / \mathrm{s}+45 \mathrm{~km} / \mathrm{hr} \\
& =180+45 \times \frac{5}{18} \mathrm{~m} / \mathrm{s} \\
& =192.5 \mathrm{~m} / \mathrm{s}
\end{aligned}\)
Speed of theifs jeep \(=153 \mathrm{~km} / \mathrm{hr}=42.5 \mathrm{~m} / \mathrm{s}\)
Velocity of bullet with respect to theif's jeep \(=192.5-42.5 \mathrm{~m} / \mathrm{s}\)
\(=150 \mathrm{~m} / \mathrm{s}\)
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