Question
Question: Two cars are moving. A along east with 10 ms<sup>-1</sup>. At any instant it is 1500 m away from the...
Two cars are moving. A along east with 10 ms-1. At any instant it is 1500 m away from the crossing. B at the same instant is 1800 m away from the crossing and is moving towards the crossing with 15ms-1. When do they come closest?
A
109.3 s
B
129.2 s
C
119.3 s
D
99.3 s
Answer
129.2 s
Explanation
Solution
x2 = (1500 – 10t)2 + (1800 – 15t)2, for x to be minimum, its first derivative should be zero. Thus dx/dt = 0
= -20 (1500 – 10t) – 30(1800 – 15t)
or t = 129.23 s