1.1 Ambala lies 250 km due north of Delhi. Lucknow lies 500 km due east of Delhi. A rail track runs between Ambala and Lucknow.
There are also rail tracks between Delhi and Lucknow and Delhi and Ambala. Plot this information on graph paper.
1.2 What is the distance a train has to travel between Ambala and Lucknow? Measure it on the graph paper.
1.3 A rail track also runs from Delhi to Gangapur, a station on the Ambala-Lucknow rail track. The unique feature of the Delhi-Gangapur track is that it is the shortest distance between Delhi and the Ambala-Lucknow track. How far is Gangapur from: (a) Delhi; (b) Ambala, and (c) Lucknow?
1.4 A train starts from Ambala for Lucknow at 9 pm travelling at 40 km per hour. Riya wants to catch this train at Gangapur. So, she starts off from Delhi in a taxi at 830 pm travelling at 60 km per hour? Will Riya be able to catch the train? If not, what is the minimum speed of the taxi to ensure that she catches the train?
1.5 Riya’s taxi reaches Gangapur but she has missed the train. She tells the taxi driver to follow the rail track and chase the train. In how much time will Riya catch up with the train?
1.6 Now, think of the vertical axis as the y-axis and the horizontal axis as the x-axis. What is the equation for the Ambala-Lucknow rail track? What is the equation of the Delhi- Gangapur rail track? What are the coordinates of Gangapur?
1.7 Hakimpur lies 200 km east and 150 km north of Delhi on the Ambala-Lucknow rail track. What is the distance between Delhi and Hakimpur?
please help i dont understand this
Answers
Given : A rail track runs between Ambala and Lucknow.
To find : distance a train has to travel between Ambala and Lucknow
How far is Gangapur from: (a) Delhi; (b) Ambala, and (c) Lucknow?
Solution:
(0 , 250)
Ambala
Gangapur (100 , 200)
250 km
Delhi 500 km Lucknow
(0,0) (500 , 0)
distance a train has to travel between Ambala and Lucknow
= √250² + 500²
= 250√ ( 1 + 4)
= 250√5 km
shortest distance between Delhi and the Ambala-Lucknow track.
means perpendicular Distance
Slope of Lucknow Ambala Track = (0 - 250)/(500 - 0) = -1/2
y - 0 = (-1/2)(x - 500)
=> 2y = -x + 500
=> x + 2y = 500 Ambala Lucknow track
Slope of Delhi Gangapur =-1/(-1/2) = 2
y - 0 = 2(x - 0)
=> y = 2x
=> x + 4x = 500
=> x = 100 & y = 200
Gangapur cordinate (100 , 200)
Delhi Gangapur distance = √(100-0)² + (200 - 0)² = 100√5 km
Gangapur Ambala = √(100-0)² + (200 - 250)² =50√5 km
Gangapur Lucknow = √(100-500)² + (200 - 0)² =200√5 km
A train starts from Ambala for Lucknow at 9 pm travelling at 40 km per hour
Ambala gangpur = 50√5 km
Time taken = 50√5/40 = 5√5/4 hr = 2.8 hrs
Time taken from Delhi Gangapur = 100√5/60 = 5√5/3 hr = 3.7 hr
2.8 + 0.5 = 3.3 < 3.7 hr so can not catch train
Please post Question one by one
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