Question

An aeroplane accelerates from rest along a runway at a rate of 4m/s⁻². It needs a velocity of 80m/s⁻¹ to take off. Find how long the runway has to be.

Answer 1

Using the kinematic equation s = v² / (2a), the runway must be 800 meters long for an aeroplane that accelerates from rest at a rate of 4m/s² to reach a take-off velocity of 80m/s.

Step-by-step explanation:

The student is inquiring about the distance an aeroplane requires to take off, given a certain acceleration and take-off speed. To calculate how long the runway has to be for an aeroplane that accelerates from rest at a rate of 4m/s² until it reaches a take-off velocity of 80m/s, we can use the kinematic equation:

s = v² / (2a)

Where s is the displacement (runway length), v is the final velocity, and a is the acceleration. Plugging in the values, we get:

s = 80² / (2 × 4)

s = 6400 / 8

s = 800 meters

Therefore, the runway must be 800 meters long for the aeroplane to take off.