Respuesta :
Answer:
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
