Q 2 A large circular field has a track along its inner boundary for conducting long distance sports events. The diameter XY of the track is 1 km. The following events were conducted.(use √ = 3.14 for calculations) Event A- Fast walking along the diameter of the field.
Event B- A 15.7 km running race along the circular track.
Event C- A 25.12 km cycling race along the circular track.
(a) If the athletes walked from X to Y then, distance and displacement covered in Event A were
(i) Both 1.57km (ii) Both 1 km (iii) 1km and 1.57km respectively (iv) 1.57km and 1 km respectively.
(b)No of rounds required to complete Event B are
(i) 10 (ii) 2.5 (iii) 5 (iv)0.5
(c)If Pihu ran at an average speed of 3.14 km/h during Event B, then she would finish the race in
(i) 0.5hours (ii) 50mins (iii)500minutes (iv) 5 hours
(d) What should the average speed of cyclist Yousef be, so that he can complete Event C in 4hours?
(i) 6.28km/h (ii) 0.628km/h (iii) 12.56km/h (iv) 1.256km/h

Explanation:

(a)

In event A , one has to walk along diameter of the field from X to Y.

In this event , walk is along a straight line , both displacement and distance covered will be same.

Distance = displacement = 1 km.

option ii is correct .

(b )

radius of circular track r = 0.5 km

length of track = circumference = 2π r

= 2 x 3.14 x .5 = 3.14 km

Length of running in event B is 15.7 km

No of rounds = 15.7 / 3.14 = 5

option iii is correct .

( c )

speed = length of race / time

time = length of race / speed

= 15. 7 km / 3.14 km /h

= 5 hours .

option iv is correct option.

(d)

In event C , length of race is 25.12 km

speed = length of race / time taken

= 25.12 km  / 4 hour

= 6.28 km/h .

Option i is correct.

(a) (ii)

(b) (iv)

(c) (i)

(d) (i)

Explanation:

diameter, XY = 1 km

Event A- Fast walking along the diameter of the field.

Event B- A 15.7 km running race along the circular track.

Event C- A 25.12 km cycling race along the circular track.

(a) When athletes walked from X to Y , the distance is equal to the displacement which is equal to the diameter = 1 km.  

Option (ii).

(b) distance = 15.7 km

distance traveled by one round = 3.14 x 1 = 3.14 km

So, the number of round complete in B = 1.57/3.14 = 0.5

option (iv).

(c)If Pihu ran at an average speed of 3.14 km/h during Event B, then she would finish the race in

time, t = 1.57/3.14 = 0.5 hours

option (i)

(d) What should the average speed of cyclist Yousef be, so that he can complete Event C in 4hours?

Distance = 25.12 km

time , t = 4 hours

Speed = 25.12 / 4 = 6.28 km/h

Option (i)

the answer would be 32*f