Turner Carrillo
06/27/2023 · Elementary School
2. An observer on the ground measures an angle of inclination of to an approaching airplane, and 10 seconds later measures an angle of inclination of \( 55^{\circ} \). If the airplane is flying at a constant speed and at a steady altitude of 6000 ft in a straight line directly over the observer, find the speed of the airplane in miles per hour. (Note: 1 mile \( =5280 \mathrm{ft} \) ).
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The speed of the airplane can be calculated using the formula \( v = \frac{\Delta d}{\Delta t} \), where \( \Delta d \) is the change in horizontal distance over 10 seconds and \( \Delta t \) is 10 seconds. The change in distance is given by \( \Delta d = \frac{6000}{\tan(\theta_1)} - \frac{6000}{\tan(55^\circ)} \). To convert the speed to miles per hour, multiply the result by \( 0.6818 \).
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