Question : Two tourist buses start from the same point and move along two roads at right angles at speeds of 48 km/hr and 36 km/hr, respectively. The distance between the buses after 15 seconds is ________.
Option 1: 175 m
Option 2: 350 m
Option 3: 250 m
Option 4: 150 m
Correct Answer: 250 m
Solution :
Speed of Bus A = 48 km/hr = $48×\frac{5}{18}=\frac{40}{3}$ m/s
Speed of bus B = 36 km/h = $36×\frac{5}{18}=10$ m/s
Distance covered by bus A in 15 sec
⇒ Distance = $\frac{40}{3}$ × 15 = 200 m
Distance covered by bus B in 15 sec
⇒ Distance = 10 × 15 = 150 m
As the two roads are at a right angle, so
⇒ Let Base = 200 m and Height = 150 m
Here, Hypotenuse = Distance between two buses
By Pythagoras theorem
Hypotenuse
2
= Base
2
+ Height
2
⇒ Hypotenuse
2
= 200
2
+ 150
2
= 40000 + 22500 = 62500
⇒ Hypotenuse
= $\sqrt{62500}$ = 250 m
Hence, the correct answer is 250 m.
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