Physics Two Dimensional Motion Question 183
Question: A jet plane flying at a constant velocity v at a height $ h=8km $ , is being tracked by a radar R located at O directly below the line of flight. If the angle $ \theta $ is decreasing at the rate of $ 0.025rad/s $ , the velocity of the plane when $ \theta =60{}^\circ $ is:
Options:
A) 1440 km/h B)960 km/h C) 1920 km/h D)480 km/h
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Answer:
Correct Answer: B
Solution:
[b] $ x=h\cot \theta $ $ \
Therefore \frac{dx}{dt}=h\frac{d( \cot \theta)}{dt} $ $ =h,,(-,\text{cose}{{c^{2}}\theta ),,\frac{d\theta }{dt} $ $ \text{or },v=h\text{ cose}{{c^{2}}\theta ,,( -\frac{d\theta }{dt} ) $ $ =(8\times 10^{3}),\text{cose}{{c^{2}}60{}^\circ \times 0.025=2666.67\text{ m/s} $ $ \text{=},,\text{960 km/h} $
BETA
