Rain is falling vertically with a speed of 35 m s-1. Winds starts blowing after sometime with a speed of 12 m s-1 in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

Question

Rain is falling vertically with a speed of 35 m s-1. Winds starts blowing after sometime with a speed of 12 m s-1 in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain? (A) sin-1((12/35)) (B) cos-1((12/35)) (C) tan-1((12/35)) (D) cot-1((12/35))

Tardigrade Admin · Accepted Answer

The velocity of the rain and the wind are represented by the vectors

v_{r}

and

v_{w}

as shown in the figure. To protect himself from the rain the boy should hold his umbrella in the direction of resultant velocity

v_{R}

. If

θ

is the angle which resultant velocity

v_{R}

makes with the vertical, then

t an θ = \frac{v _{w}}{v _{r}} = \frac{12}{35}

or

θ = t a n^{- 1} (\frac{12}{35})

Q. Rain is falling vertically with a speed of $35 m s^{- 1}$ . Winds starts blowing after sometime with a speed of $12 m s^{- 1}$ in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

$s i n^{- 1} (\frac{12}{35})$

$co s^{- 1} (\frac{12}{35})$

$t a n^{- 1} (\frac{12}{35})$

$co t^{- 1} (\frac{12}{35})$

Q. Rain is falling vertically with a speed of 35ms−1. Winds starts blowing after sometime with a speed of 12ms−1 in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

sin−1(3512​)

cos−1(3512​)

tan−1(3512​)

cot−1(3512​)

Q. Rain is falling vertically with a speed of $35 m s^{- 1}$ . Winds starts blowing after sometime with a speed of $12 m s^{- 1}$ in east to west direction. At what angle with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

$s i n^{- 1} (\frac{12}{35})$

$co s^{- 1} (\frac{12}{35})$

$t a n^{- 1} (\frac{12}{35})$

$co t^{- 1} (\frac{12}{35})$