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Q.
An aeroplane executes a horizontal loop at a speed of $720 \,kmph$ with its wings banked at $45^\circ$, What is the radius of the loop ? Take $g=10\, ms ^{-2}$
Given, execution of horizontal loop
at $v=720\, km / h =720 \times \frac{5}{18}$
$=40 \times 5=200 m / s$
$g=10 \,m / s ^{2},\, \theta =45^{\circ}$
As we know that
$\tan \theta =\frac{v^{2}}{r g}$
$r =\frac{v^{2}}{g \,\tan\, \theta}$
$=\frac{(200)^{2}}{10 \times \tan 45^{\circ}}=\frac{40000}{10 \times 1}$
$=4000\, m =4\, km$