An airplane lands on a runway at a speed of 180 km/hr. It is brought to a stop uniformly in 30seconds. What distance does it cover on the runway before coming to rest?
To find the distance covered by the airplane before coming to rest, we need to calculate the deceleration first.
The change in velocity can be calculated by converting the initial speed to m/s and subtracting the final speed (0 m/s).
180 km/hr = (180 * 1000) / (60 * 60) = 50 m/s
Using the equation:
Change in velocity (Δv) = final velocity (v) - initial velocity (u)
Δv = 0 m/s - 50 m/s
The time taken for the airplane to stop is given as 30 seconds.
The deceleration (a) can be calculated by using the formula:
a = Δv / t
a = (0 m/s - 50 m/s) / 30 s
a = (-50 m/s) / 30 s
To find the distance (d) covered by the airplane before coming to rest, we can use the formula:
d = (u^2 - v^2) / (2a)
d = (50^2 - 0^2) / (2 * (-50/30))
Simplifying the equation, we get:
d = (2500) / (-5/3)
d = -7500 / 5
d = -1500 meters (taking direction into account)
Therefore, the airplane covers a distance of 1500 meters on the runway before coming to rest.
To find the distance covered by the airplane before coming to rest, we will use the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Given:
Initial velocity (u) = 180 km/hr
Acceleration (a) = -final velocity (v) = 0 km/hr (since it comes to rest)
Time (t) = 30 seconds
First, we need to convert the initial velocity from km/hr to m/s:
1 km/hr = 1/3.6 m/s
So, initial velocity (u) = 180 km/hr = (180/3.6) m/s = 50 m/s
Given that final velocity (v) = 0 km/hr, we can find the acceleration using the formula:
v = u + at
0 = 50 + a * 30
a = -50/30 = -5/3 m/s^2
Now, we can substitute the values into the distance formula:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
distance = (50 * 30) + (0.5 * (-5/3) * 30^2)
distance = 1500 + (0.5 * (-5/3) * 900)
distance = 1500 - (5/6) * 900
distance = 1500 - (5 * 150)
distance = 1500 - 750
distance = 750 meters
Therefore, the airplane covers a distance of 750 meters on the runway before coming to rest.