Question

Starting from rest, Christina experiences 24.5 m/s2 of acceleration to take off from an aircraft carrier for 5 seconds. How long does the runway need to be? Round to the nearest meter.

Answer 1

Answer:

The length of the runway to the nearest meter is 306 m.

Explanation:

Given:

Initial velocity of Christina is, $u=0\ m/s(Rest)$

Time taken is, $t=5\ s$

Acceleration experienced by Christina is, $a=24.5\ m/s^2$

The length of the runway is, $d=?$

Now, we use Newton's equation of motion that relates the distance, initial velocity, time and acceleration.

So, we have the following equation of motion:

$d=ut+\frac{1}{2}at^2$

Plug in all the given values and solve for 'd'. This gives,

$d=0+\frac{1}{2}\times 24.5\times 5^2\\\\d=\frac{1\times 24.5\times 25}{2}\\\\d=\frac{612.5}{2}\\\\d=306.25\approx 306\ m(\textrm{Rounding to nearest meter})$

Therefore, the length of the runway to the nearest meter is 306 m.