# Find The rate at which the observer’s head is tilting when the angle of inclination is 60 degree:

Step-by-step solution-:

The Given that:

x=\frac{3}{2\tan{(\theta)}}

The Average Speed is:

\frac{dx}{dt}=650~km/h

Recall The Chain Rule:

\frac{dx}{dt}=\frac{dx}{d\theta}\cdot \frac{d\theta}{dt}

Let be y :

y=\frac{d\theta}{dt}

Substitute the

\frac{d\theta}{dt}=y, \theta=\frac{\pi}{3}, {\frac{dx}{d\theta}=-\frac{3}{2\sin^{2}{(\theta)}}}

into the above:

\textcolor{primary}{650}=-\frac{3}{2\sin^{2}{\textcolor{secondary}{(\frac{\pi}{3})}}}\cdot \textcolor{tertiary}{y}

After simplifying we get,

Therefore, The value of y is:

y=-325~radian ~per~hour

y=-(325\cdot \frac{1}{3600})~radian ~per~second

Convert the radian per hour to degrees per second

Recall the Converting Degrees and Radians:

y=-(325\cdot \frac{1}{3600}\cdot \frac{180^{\circ}}{\pi})~degrees ~per~second

After simplifying we get,

Therefore, The value of y is:

y\approx-5

Rate is decreased by 5~degrees ~per~second:

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