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A jet plane lands with a speed of 110 m/s and can accelerate uniformly at a maximum rate of -5.0 m/s2 as it

comes to rest. Can this plane land at an airport where the runway is 0.8 km long?

User Gac
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1 Answer

3 votes

Final answer:

The jet plane, with an initial speed of 110 m/s and deceleration of -5.0 m/s², requires 1.21 km to come to a stop. Therefore, it cannot land safely on a 0.8 km runway.

Step-by-step explanation:

A student has asked if a jet plane landing with a speed of 110 m/s and able to accelerate uniformly at a maximum rate of -5.0 m/s2 can stop on a runway that is 0.8 kilometers long. To solve this, we can use the kinematic equation that relates initial velocity, acceleration, and the distance traveled:

d = vit + (1/2)at2

We have the initial velocity (​vi) of 110 m/s, and we need to find the time (​t) it takes for the plane to stop (final velocity, vf = 0 m/s). Since the acceleration (a) is -5.0 m/s2, we can rearrange the equation to solve for time:

t = (vf - vi)/a

By substituting the values, we find that the time required to stop is:

t = (0 - 110)/(-5) = 22 seconds

Now we can calculate the distance the plane will travel during this time:

d = (110)(22) + (1/2)(-5)(22)2

After calculation, this gives us a distance of:

d = 1210 m, or 1.21 km

Since 1.21 km is greater than the available 0.8 km runway, the plane cannot safely land on that runway.

User Himanshu Poddar
by
7.7k points
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