An aircraft executes a horizontal loop at a speed of 720 km h-1 with its wings banked at 15°. What is the radius of the loop? (Take g=10 m s-2, tan 15°=0.27)

Question

An aircraft executes a horizontal loop at a speed of 720 km h-1 with its wings banked at 15°. What is the radius of the loop? (Take g=10 m s-2, tan 15°=0.27) (A) 14.8 km (B) 14.8 m (C) 29.6 km (D) 29.6 m

Tardigrade Admin · Accepted Answer

Here, v=720 km h-1 =720×(5/18)m s-1 =200 m s-1 θ=15°, g=10 m s-2 As tan θ=(v2/rg) ∴ r=(v2/tan θ g) =((200 m s-1)2/tan 15°×10 m s-2) =14815 m=14.8 km

Q. An aircraft executes a horizontal loop at a speed of $720 km$ $h^{- 1}$ with its wings banked at $1 5^{°}$ . What is the radius of the loop? (Take $g = 10 m s^{- 2}, t an 1 5^{\circ} = 0.27$ )

$14.8 km$

$14.8 m$

$29.6 km$

$29.6 m$

Here, $v = 720 km$ $h^{- 1}$ $= 720 \times \frac{5}{18} m$ $s^{- 1}$ $= 200 m$ $s^{- 1}$
$θ = 1 5^{\circ}$ , $g = 10 m s^{- 2}$ As tan $θ = \frac{v ^{2}}{r g}$
$∴$ $r = \frac{v ^{2}}{t an θ g}$ $= \frac{( 200 m s ^{- 1} ) ^{2}}{t an 1 5 ^{\circ} \times 10 m s ^{- 2}}$ $= 14815 m = 14.8 km$

Q. An aircraft executes a horizontal loop at a speed of 720km h−1 with its wings banked at 15°. What is the radius of the loop? (Take g=10ms−2,tan15∘=0.27)

14.8km

14.8m

29.6km

29.6m