A person sees a lightning bolt pass close to an airplane that is flying in the d

Question

A person sees a lightning bolt pass close to an airplane that is flying in the distance. The person hears thunder 7.0 s after seeing the bolt and sees the airplane overhead 13 s after hearing the thunder. The speed of sound in air is 1100 ft/s.

(a) Find the distance of the airplane from the person at the instant of the bolt. (Neglect the time it takes the light to travel from the bolt to the eye.)

(b) Assuming that the plane travels with a constant speed toward the person, find the velocity of the airplane.
ft/s

(c) Look up the speed of light in air, and defend the approximation used in (a).

Explanation / Answer

a) Use the speed of sound to find the distance. The thunder was heard 6 seconds later. That means you were: 11,00ft/s * 6 s = 6,600 ft away from the plane when lightnining struck. b) Since the plane was 6600ft away, and 10s after the thunder it is right above you, it means that it travelled 6600 ft in (10+6)s. Remember, you need to account for the time the plane travelled before thunder hit!! Thus the plane's velocity is : 6600ft/16s = 4125 m/s c) speed of light in air: 983571056.430 ft/s. Since this is so fast, the accuracy is very high and the time taken is almost instantaneous. The time it took for the light to reach your eyes was 6600ft/983571056.430ft/s = 6.7102 *10^-6 s. This is nearly impossible for us to measure without high tech tools, so we resort to an approximation of the speed of sound in order to do the calculations.

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