Question

an aeroplane on a runway starts from rest a picks up a velocity of 180 km+h and takes off . in doing so , it covers a runway of 1.5 km . calculate (a) the uniform acceleration acting on the aeroplane and (b) the time in which it takes off .

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{initial}\mathrm{velocity},\mathrm{u}=0 \\ \mathrm{final}\mathrm{velocity},\mathrm{v}=180\mathrm{km}/\mathrm{h}=50\mathrm{m}/\mathrm{s} \\ \mathrm{distance},\mathrm{s}=1.5\mathrm{km} \\ \mathrm{we}\mathrm{know}\mathrm{that}, \\ {\mathrm{v}}^2-{\mathrm{u}}^2=2\mathrm{as} \\ {\left(180\right)}^2-{\left(0\right)}^2=2\times \mathrm{a}\times 1.5 \\ \mathrm{a}=\frac{32400}{3}=10800\mathrm{km}/{\mathrm{h}}^2 \\ \mathrm{or},\mathrm{a}=10800\times \frac{1000}{{\left(3600\right)}^2}\mathrm{m}/{\mathrm{s}}^2 \\ \mathrm{or},\mathrm{a}=0.833\mathrm{m}/{\mathrm{s}}^2 \\ \mathrm{Also},\mathrm{v}=\mathrm{u}+\mathrm{at} \\ 50=0+0.833\times \mathrm{t} \\ \mathrm{t}=\frac{50}{0.833}=60.02\mathrm{s} \end{gathered}$$