A jet plane lands with a speed of 110 m/s and can decelerate uniformly at a maximum rate of 5.7m/s^2 as it comes to rest.
Can this plane land at an airport where the runway is 0.91 km long?
I have to answer by Calculating...HELP!
Vf^2 = Vo^2 + 2ad = 0,
(110)^2 + 2 * (-5.7)d = 0,
12100 - 11.4d = 0,
-11.4d = -12100,
d = -12100 / -11.4 = 1061.4m = 1.061km.
NO, the runway is too short
NOTE:Check your 1-11-11,7:44pm post.
To determine whether the plane can land at the airport, we need to calculate the distance it needs to decelerate to come to a stop and compare it to the length of the runway.
First, let's convert the speed and runway length into consistent units.
The speed of the plane is given in meters per second (m/s), and the runway length is given in kilometers (km). We should convert the 0.91 km into meters to match the speed unit.
1 km is equal to 1000 meters, so 0.91 km is equal to 0.91 * 1000 = 910 meters.
Next, we can use the formula for distance traveled during deceleration:
distance = (initial velocity^2) / (2 * acceleration)
Given:
Initial velocity = 110 m/s
Acceleration = -5.7 m/s^2 (negative because deceleration)
Plugging in the values, we get:
distance = (110^2) / (2 * -5.7)
Calculating this expression:
distance = 12100 / -11.4
distance ≈ -1058.77 meters
The calculated negative distance indicates that the plane needs to decelerate beyond the length of the runway. Therefore, the plane cannot land safely on the runway, given the specified conditions.