An aircraft has a take-off speed 180km/h and length 250m from the start just before take-off a serious snag is detected in the engine and the aircraft failed to take-off. There is a wall at a distance 'd' = 230m ahead of the take-off point. The pilot applies breaks which produces as much retardation as the acceleration of the aircraft and succeeds in avoiding the crash on the wall. What is the reaction time of the pilot?? Please help me in solving it!! How to solve it? Method of solving it!!
d = 230 m = Required stopping distance.
Vo = 180km/h = 180,000m/3600s = 50m/s = Initial velocity before take-off.
V^2 = Vo^2 + 2a*d.
0 = 50^2 + 2a*230
-460a = 2500
a = -5.43m/s^2.
V = Vo + a*t.
0 = 50 - 5.43t
t = ?.
To solve this problem, we can use the equations of motion to find the reaction time of the pilot.
Let's break down the solution into smaller steps:
Step 1: Find the initial velocity (u) of the aircraft.
Given that the take-off speed is 180 km/h, we need to convert it to m/s.
180 km/h = (180 * 1000) / (60 * 60) = 50 m/s.
So, the initial velocity (u) of the aircraft is 50 m/s.
Step 2: Find the final velocity (v) of the aircraft.
Since the aircraft failed to take off, the final velocity (v) is 0 m/s.
Step 3: Find the acceleration (a) of the aircraft.
The pilot applies the brakes, which produces the same retardation (deceleration) as the acceleration of the aircraft. Therefore, the acceleration (a) is equal in magnitude but opposite in sign to the acceleration during takeoff.
Step 4: Find the distance (s) traveled by the aircraft.
The distance (s) can be calculated using the equation:
s = (v^2 - u^2) / (2a)
Here, s is the distance traveled, v is the final velocity, u is the initial velocity, and a is the acceleration.
Since v = 0 m/s and u = 50 m/s, the equation simplifies to:
s = (0^2 - 50^2) / (2a)
We can rearrange this equation to solve for the acceleration (a):
a = -50^2 / (2s)
Step 5: Find the acceleration (a) caused by the braking.
Using the distance given in the problem, s = 230m, we can substitute it into the equation to find the acceleration:
a = -50^2 / (2 * 230)
Step 6: Find the time taken to come to a stop.
The time (t) taken to come to a stop can be calculated using the equation:
t = (v - u) / a
As v = 0 m/s and u = 50 m/s, the equation simplifies to:
t = -50 / a
Step 7: Calculate the reaction time.
Since the pilot needs to react immediately after detecting the snag, the total time taken will be the reaction time.
Hence, the reaction time of the pilot is -50 / a.
Solving this equation will provide the value of the pilot's reaction time.