# NCERT Class 11 Physics Solutions: Chapter 4 – Motion in a Plane Part 5

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Question 4.11:

A passenger arriving in a new town wishes to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is

(a) The average speed of the taxi.

(b) The magnitude of average velocity ? Are the two equal?

(a) ) The average speed of the taxi:

Total distance travelled

Total time taken

∴ Average speed of the taxi

(b) The magnitude of average velocity:

Distance between the hotel and the station = 10 km = Displacement of the car.

∴ Average velocity

Therefore,

The two physical quantities (average speed and average velocity) are not equal.

Question 4.12:

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

The described situation is shown in the given figure:

Here,

= Velocity of the cyclist

= Velocity of falling rain

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.

Hence,

The woman must hold the umbrella toward the south, at an angle of nearly 18° with the vertical.

Question 4.13:

A man can swim with a speed of 4.0 km/h in still water. How long does he take to cross a river 1.0 km wide if the river flows steadily at 3.0 km/h and he makes his strokes normal to the river current? How far down the river, does he go when he reaches the other bank?