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Velocity

A paraglider ...

Question

A paraglider to show his skills jumped from a very tall building. After $2 s$ of free fall he sees a balloon rising with the constant speed of 2 $m s^{- 1}$ at a distance $2 m$ as shown. The relative angular velocity of balloon w.r.t. person at this instant will be :

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Solution

Initial velocity of person $u = 0 m / s$
Velocity after 2 seconds, $v = u + g t = 0 + 10 \times 2 = 20 m / s$ (downwards)
Velocity of balloon $V_{b} = 2 m / s$ (upwards)
Relative velocity of balloon w.r.t. person $V_{r e l} = 2 - (- 20) = 22 m / s$
Relative angular velocity $w_{r e l} = \frac{V_{r e l}}{r} = \frac{22}{2} = 11 r a d / s$

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