Rain is falling vertically with a speed of $25 m / s$ . A woman rides a bicycle with a speed of $8 m / s$ in the north to south direction. What is the direction in which she holds her umbrella to protect herself from the rain?

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Solution

The velocity of the cyclist be $v_{c}$

The velocity of the rain is $v_{r}$

The relative velocity will be

$v = v_{r} - v_{c}$

$v = 25 - 8 m / s$

Hence the relative velocity is $25 - 8 m / s$

To find the angle of the umbrella

$tan θ = \frac{v_{c}}{v_{r}}$

$θ = {tan}^{-} (\frac{8}{17})$

The angle is ${43.9}^{\circ}$

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Rain is falling vertically with a speed of 25m/s . A woman rides a bicycle with a speed of 8m/s in the north to south direction. What is the direction in which she holds her umbrella to protect herself from the rain?

The velocity of the cyclist be vc The velocity of the rain is vr The relative velocity will be v=vr−vc v=25−8m/s Hence the relative velocity is25−8m/s To find the angle of the umbrella tanθ=vcvr θ=tan−(817) The angle is43.9∘

Rain is falling vertically with a speed of $25 m / s$ . A woman rides a bicycle with a speed of $8 m / s$ in the north to south direction. What is the direction in which she holds her umbrella to protect herself from the rain?