Question

A plane with a speed of 75m/s is going to travel along a runway of 25km, If it makes an acceleration of 1.3(m/s)/s, will it use the runway safely? Justify your answer.

Answer 1

Answer on Question#38486 – Physics – Mechanics | Kinematics | Dynamics

A plane with a speed of $75\,\mathrm{m/s}$ is going to travel along a runway of $25\,\mathrm{km}$. If it makes an acceleration of $1.3\,\mathrm{m/s/s}$, will it use the runway safely? Justify your answer.

Solution:

$$a = 1.3\,\frac{\mathrm{m}}{\mathrm{s}^2} - \text{decceleration of the plane};$$ $$V_0 = 75\,\frac{\mathrm{m}}{\mathrm{s}} - \text{initial velocity of the plane};$$

Equation of motion for the plane for first distance $d$:

$$d = V_0 t - \frac{a t^2}{2}$$

Rate equation for the plane for this distance ($V_1 = 0$ – velocity after time $t$):

$$V_1 = V_0 - a t$$ $$V_0 - a t = 0$$ $$t = \frac{V_0}{a}$$

(2)in(1):

$$d = V_0 \cdot \frac{V_0}{a} - \frac{a \left(\frac{V_0}{a}\right)^2}{2} = \frac{V_0^2}{2a} = \frac{(75\,\frac{\mathrm{m}}{\mathrm{s}})^2}{2 \cdot 1.3\,\frac{\mathrm{m}}{\mathrm{s}^2}} = 2160\,\mathrm{m}$$

Answer: plane will use the runway safely (travelled distance $2.16\,\mathrm{km} < 25\,\mathrm{km}$).