Question

A car on the cross road is moving towards east at
a speed of 40 km/hr. Another car which is 1 km
south of the crossing is approaching the crossing
with the same speed. Their closest distance of
approach will be
(1) 1 km
(2) Ta km
(3) V2 km
(4) 212 km
Road New Delhi-110005 Ph. 011-47623456
​

Answer 1

Answer:

1/√2  km  = 0.707 km

Explanation:

A car on the cross road is moving towards east at

a speed of 40 km/hr. Another car which is 1 km

south of the crossing is approaching the crossing

with the same speed. Their closest distance of

approach will be

Distance of Car A  from crossing =  40 T    

Distance of Car B  from crossing = 1 - 40T

Distance between Car A & Car B =  √ ((40T)² + (1 - 40T)²)

= √ 1600T² + 1 + 1600T² - 80T

= √ 3200T² - 80T + 1

d(D)/dt  =  (1/2) ( 6400T - 80)

d(D)/dt  = 0

=> T = 80/6400

=> T = 1/80 hr

=> 40T = 1/2

d(D)/dt² = 3200 ( +ve)

so T = 1/80 will give minimum distance

Min Distance between Car A & B =  √ ((1/2)² + (1 - 1/2)²)

= √ (1/4 +1/4)

= √1/2

= 0.707 km