Question

A person sees in the distance a lightning bolt pass close to a low flying airplane. The person hears thunder 5.6 s after seeing the bolt, and sees the airplane overhead 13 s after hearing the thunder. 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. The speed of sound in air is 1100 ft/s. Find the velocity of the airplane

Answer 1

The distance of the airplane from the person when the lightning bolt strikes is 6160 feet. The velocity of the airplane is approximately 473.85 ft/s, calculated using the time it takes for the sound of thunder to reach the observer and the time it takes for the airplane to fly overhead.

Step-by-step explanation:

The distance to the airplane from the person at the instant of the lightning bolt can be found using the speed of sound and the time delay between seeing the lightning and hearing the thunder. Knowing that the speed of sound in air is 1100 ft/s and that the thunder is heard 5.6 s after the lightning is seen, we can calculate the distance (d) as:

d = speed of sound × time delay = 1100 ft/s × 5.6 s = 6160 ft

Next, to find the velocity of the airplane, we use the time taken for the airplane to travel from the position of the lightning bolt to being directly overhead, which is 13 s after hearing the thunder. If the plane traveled 6160 ft in this time, its velocity (v) is:

v = distance / time = 6160 ft / 13 s ≈ 473.85 ft/s

Answer 2

Step-by-step explanation:

velocity v = Δx/Δt

Δx is the change in displacement

Δt is the change in time

Δx = vΔt

Given v = 1100ft/s

Δt = t2-t1

Δt = 13-5.6

Δt = 7.4s

Δx = 1100*7.4

Δx = 8,140ft

Hence the distance of the airplane from the person at the instant of the bolt is 8,140ft

Since the air moves at constant speed, it means the speed is not chnaging hence the velocity of the air v is the same as the constant speed.

velocity of the airplane vp = Δx/Δt

Δx = 8,140ft

Δt = t2+t1

Δt = 13+5.6

Δt = 18.6s

Substituting the given values into the formula vp = Δx/Δt

vp = 8,140/18.6

vp = 437.63m/s

Hence the velocity of the airplane is 437.63m/s