ccording to Richard Graham in "SR-71 Revealed: The Inside Story", the Lockheed SR-71 Reconnaissance plane accelerates from a standing start to a speed of Mach 3 (3 times the speed of sound) "in about 14 minutes". (During that time it also climbs to an altitude of about 70,000 feet, so the acceleration is not as impressive as you might otherwise expect.) Assuming that the time is exactly 14 minutes, and the speed of sound is 1100 feet per second, this is an average acceleration of ? feet per second squared. Assuming that the acceleration is constant, during that time your SR-71 covers a distance of ? miles.

Question

ccording to Richard Graham in "SR-71 Revealed: The Inside Story", the Lockheed SR-71 Reconnaissance plane accelerates from a standing start to a speed of Mach 3 (3 times the speed of sound) "in about 14 minutes". (During that time it also climbs to an altitude of about 70,000 feet, so the acceleration is not as impressive as you might otherwise expect.) Assuming that the time is exactly 14 minutes, and the speed of sound is 1100 feet per second, this is an average acceleration of ? feet per second squared. Assuming that the acceleration is constant, during that time your SR-71 covers a distance of ? miles.

Answer 1

acceleration=change in velocity/timeinseconds

Answer 2

To find the average acceleration of the SR-71 aircraft, we can use the formula:

average acceleration = change in velocity / time taken

First, let's calculate the change in velocity. The SR-71 goes from a standing start to a speed of Mach 3, which is 3 times the speed of sound. Given that the speed of sound is 1100 feet per second, the final velocity will be 3 * 1100 = 3300 feet per second.

The initial velocity is 0 since it starts from a standing start. Therefore, the change in velocity is 3300 - 0 = 3300 feet per second.

The time taken is given as 14 minutes. However, we need to convert this to seconds, as the units for time and velocity should be the same for the calculation. There are 60 seconds in a minute, so 14 minutes * 60 seconds per minute = 840 seconds.

Now let's find the average acceleration:

average acceleration = change in velocity / time taken
= 3300 ft/s / 840 s
≈ 3.93 ft/s²

Therefore, the average acceleration of the SR-71 aircraft is approximately 3.93 feet per second squared.

To find the distance covered during this time, we need to use the formula:

distance = initial velocity * time taken + (1/2) * acceleration * (time taken)²

Since the initial velocity is 0, the formula simplifies to:

distance = (1/2) * acceleration * (time taken)²

Let's calculate the distance:

distance = (1/2) * 3.93 ft/s² * (840 s)²
≈ 1,850,464 feet
≈ 350 miles (approximately)

Therefore, during the 14 minutes, the SR-71 aircraft covers a distance of approximately 350 miles.