To find the acceleration of the plane, we can use the formula:
acceleration = (final velocity - initial velocity) / time
First, let's convert the take-off speed from kilometers per hour (km/hr) to meters per second (m/s).
1 km/hr = (1000 m) / (60 s) = 16.67 m/s (approx.)
So, the take-off speed of 170 km/hr is approximately 170 * 16.67 = 2833.3 m/s.
Since the plane starts from rest, the initial velocity is 0 m/s.
Now we can calculate the time it takes for the plane to reach take-off speed.
We can use the equation of motion:
s = ut + (1/2)at^2
Where:
s = distance (145 meters)
u = initial velocity (0 m/s)
a = acceleration (unknown)
t = time (unknown)
By rearranging the equation, we have:
t^2 = (2s) / a
Substituting the known values:
t^2 = (2 * 145 m) / a
t^2 = 290 m / a
We can now find the time it takes for the plane to become airborne by calculating the square root of both sides:
t = √(290 m / a)
To find the acceleration, plug in the values of time (t = √(290 m / a)) and final velocity (v = 2833.3 m/s) into the acceleration formula:
2833.3 m/s = (final velocity) - (initial velocity)
= (a)(t)
So, the equation becomes:
2833.3 m/s = a * √(290 m / a)
To solve for acceleration (a), we need to square both sides to get rid of the square root:
(2833.3 m/s)^2 = (a * √(290 m / a))^2
8001208.89 = a^2 * (√(290/a))^2
8001208.89 = a^2 * (290/a)
8001208.89 = 290a
Now, solving for acceleration (a):
a = 8001208.89 / 290
a ≈ 27591.42 m/s^2 (approx.)
Therefore, the acceleration of the plane is approximately 27591.42 m/s^2.
Next, we can find the time it takes for the plane to become airborne by plugging this acceleration value into the equation for time:
t = √(290 m / a)
t = √(290 m / 27591.42 m/s^2)
t ≈ 0.0496 seconds
Therefore, it takes approximately 0.0496 seconds (or 49.6 milliseconds) for the plane to become airborne.
Steve 
Explain Bot