A certain aircraft has a liftoff speed of 126 km/h.
(a) What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of 244 m?
m/s2
(b) How long does it take the aircraft to become airborne?
s
To solve this problem, we can use the following kinematic equation:
v² = u² + 2as
Where:
v = final velocity (0 m/s, as the aircraft becomes airborne)
u = initial velocity (126 km/h = 35 m/s)
a = acceleration (what we're trying to find)
s = displacement (244 m)
(a) To find the minimum constant acceleration required, we need to rearrange the equation to solve for 'a':
a = (v² - u²) / (2s)
Substituting the given values into the equation, we have:
a = (0 - (35 m/s)²) / (2 * 244 m)
Simplifying the equation:
a = (-1225 m²/s²) / (488 m)
a ≈ -2.51 m/s²
Since the acceleration cannot be negative, we take the magnitude of the value, resulting in the minimum constant acceleration required being approximately 2.51 m/s².
(b) To find the time it takes for the aircraft to become airborne, we can use the following kinematic equation:
v = u + at
Rearranging the equation to solve for 't':
t = (v - u) / a
Substituting the given values:
t = (0 m/s - 35 m/s) / (-2.51 m/s²)
Simplifying the equation:
t ≈ 13.94 s
Therefore, it takes approximately 13.94 seconds for the aircraft to become airborne.