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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?
- a)about 18∘ with the vertical, towards the south
- b)about 28∘ with the vertical, towards the south
- c)about 28∘ with the vertical, towards the north
- d)about 18∘ with the vertical, towards the north
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Rain is falling vertically with a speed of 30 ms−1. A woman ride...
In order to protect herself from the rain, the woman must hold her umbrella in the direction of the relative velocity (v) of the rain with respect to the woman.
v = vr + (-vc)
= 30 + (-10) = 20 m/s
tan θ = vc / vr = 10 / 30
θ = tan^-1 (1 / 3)
= tan^-1 (0.333) ≈ 18 degree
Hence, the woman must hold the umbrella toward the south, at an angle of nearly 18 degree with the vertical.
Most Upvoted Answer
Rain is falling vertically with a speed of 30 ms−1. A woman ride...
To determine the direction in which the woman should hold her umbrella, we need to consider the velocities of rain and the woman on the bicycle.
Given:
Velocity of rain (v_rain) = 30 m/s, vertically downward (negative direction)
Velocity of woman (v_woman) = 10 m/s, in the north to south direction
We can break down the velocities into their respective components:
v_rain = 0 m/s in the north-south direction and -30 m/s in the vertical direction
v_woman = 10 m/s in the north-south direction and 0 m/s in the vertical direction
The direction in which the umbrella should be held is the direction that opposes the relative velocity of rain with respect to the woman. This is because we want to minimize the amount of rain that falls on the woman.
To find the relative velocity of rain with respect to the woman, we subtract the velocity of the woman from the velocity of rain:
v_relative = v_rain - v_woman
v_relative = (0 - 10) m/s in the north-south direction and (-30 - 0) m/s in the vertical direction
v_relative = -10 m/s in the north-south direction and -30 m/s in the vertical direction
Since the relative velocity is in the southward direction, the woman should hold her umbrella towards the south.
Now, we need to determine the angle at which the umbrella should be held with respect to the vertical direction.
The tangent of this angle can be found using the components of the relative velocity:
tan(theta) = (vertical component of relative velocity) / (north-south component of relative velocity)
tan(theta) = (-30 m/s) / (-10 m/s)
tan(theta) = 3
Solving for theta, we find:
theta = arctan(3)
Using a calculator, we find:
theta ≈ 71.6°
Therefore, the woman should hold her umbrella at an angle of approximately 71.6° with the vertical, towards the south.
However, none of the given options match this angle exactly. Option A, which states that the woman should hold her umbrella at an angle of about 18° with the vertical, towards the south, is incorrect. The correct answer should be the angle of approximately 71.6°, which is not provided in the given options.
Given:
Velocity of rain (v_rain) = 30 m/s, vertically downward (negative direction)
Velocity of woman (v_woman) = 10 m/s, in the north to south direction
We can break down the velocities into their respective components:
v_rain = 0 m/s in the north-south direction and -30 m/s in the vertical direction
v_woman = 10 m/s in the north-south direction and 0 m/s in the vertical direction
The direction in which the umbrella should be held is the direction that opposes the relative velocity of rain with respect to the woman. This is because we want to minimize the amount of rain that falls on the woman.
To find the relative velocity of rain with respect to the woman, we subtract the velocity of the woman from the velocity of rain:
v_relative = v_rain - v_woman
v_relative = (0 - 10) m/s in the north-south direction and (-30 - 0) m/s in the vertical direction
v_relative = -10 m/s in the north-south direction and -30 m/s in the vertical direction
Since the relative velocity is in the southward direction, the woman should hold her umbrella towards the south.
Now, we need to determine the angle at which the umbrella should be held with respect to the vertical direction.
The tangent of this angle can be found using the components of the relative velocity:
tan(theta) = (vertical component of relative velocity) / (north-south component of relative velocity)
tan(theta) = (-30 m/s) / (-10 m/s)
tan(theta) = 3
Solving for theta, we find:
theta = arctan(3)
Using a calculator, we find:
theta ≈ 71.6°
Therefore, the woman should hold her umbrella at an angle of approximately 71.6° with the vertical, towards the south.
However, none of the given options match this angle exactly. Option A, which states that the woman should hold her umbrella at an angle of about 18° with the vertical, towards the south, is incorrect. The correct answer should be the angle of approximately 71.6°, which is not provided in the given options.
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Rain is falling vertically with a speed of 30 ms−1. A woman rides a bicycle with a speed of 10 ms−1in the north to south direction. What is the direction in which she should hold her umbrella?a)about18∘with the vertical, towards the southb)about28∘with the vertical, towards the southc)about28∘with the vertical, towards the northd)about18∘with the vertical, towards the northCorrect answer is option 'A'. Can you explain this answer?
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