Question

Rain is falling vertically with a speed of 30 m s⁻¹. A woman rides a bicycle with a speed of 10 m s⁻¹ in the north to south direction. What is the direction in which she should hold her umbrella?

Answer 1

Hii dear,

# Answer- Towards south at an angle of 18.3°.

# Given-
Velocity of woman cyclist,
vc = 10 m/s.
Velocity of falling rain,
vr = 30 m/s

# Calculations-
To protect from rain, woman must hold her umbrella in the direction of relative velocity of of rain wrt woman.

Angle of relative velocity vector is given by,
tanθ = vc/vr
tanθ = 10/30
tanθ = 1/3
Taking inverse,
θ = 18.3°.

Thus, a woman must hold her umbrella towards south at angle of 18.3° with horizontal.

Hope that helps you...

Answer 2

Answer:

Angle, $\theta=18.4^0$

Explanation:

It is given that, rain is falling vertically with a speed of 30 m/s. The speed of woman is 10 m/s. We have to find the direction in which she should hold the umbrella.

From the attached figure, $v_c,v_r$ are the velocities of cyclist and velocity of rain respectively.

So, $tan\ \theta=\dfrac{v_c}{v_r}$

$tan\ \theta=\dfrac{10}{30}$

$\theta=18.4^0$

So, she should hold umbrella toward sound at and angle of 18.4° with y - axis. Hence, this is the required solution.