A jet is flying from atlanta to gulfport and is cruising at Mach .79 or 844 km/hr. During the last 89 km it reduces its speed for landing at a rate of -2780 km/hr^2. How long will it take for the jet to reach landing speed? What was the landing speed of the jet?

The time it takes for the jet to reach landing speed is approximately 0.136 hours which is approximately 489 seconds

The landing speed is approximately 466.365 km/hr

Explanation:

The given parameters are;

The initial cruising speed of the jet = Mach 0.79 = 844 km/hr

The rate of speed reduction in the last 89 km = -2780 km/hr²

The distance it  takes the jet to reduce its speed for landing = 89 km

Given the above information,  we make use of the following equation of motion;

s = u·t - 1/2·a·t²

v² = u² - 2·a·s

Where;

s = The distance over which the acceleration (deceleration) is applied = 89 km

u = The initial velocity = 844 km/hr

t = The time taken for the accelerating/decelerating motion

v = The final velocity (landing speed)

Substituting the values gives;

v² = 844² - 2·(2780)·89 = 217496

v = √217496 = 466.365 km/hr

v ≈ 466.365 km/hr

Therefore, the landing speed, v  ≈ 466.365 km/hr

The time it takes is given by the equation, v = u - a·t

Therefore;

t = (u - v)/a = (844 - 466.365)/2780 ≈ 0.136 hours

The time it takes for the jet to reach landing speed ≈ 0.136 hours

From, s = u·t - 1/2·a·t², we have

89 = 844·t - 1/2 × 2780 × t²

89 = 844·t - 1390 × t²

1390 × t² - 844·t + 89 = 0

Solving with an online application gives;

t = 211/695 + (√(27187/2))/695 = 0.4715 hours or t = 211/695 - (√(27187/2))/695 = 0.136 hours

We note that the second time is for the time it will take the jet to get back to 89 km after reaching a speed of 0

Therefore, the correct time is t = 0.136 hours

The time it takes for the jet to reach landing speed ≈ 0.136 hours