Question

The distance between two trucks moving towards each other is decreasing at the rate of $10 \,m / s$. If these trucks travel with same speeds in same direction the separation increases at the rate of $5\, m / s$. The velocity of the trucks are:

• A. $V_{1}=8.5\, m / s , V _{2}=1.5 \,m / s$
• B. $V_{1}=7.5\, m / s , V _{2}=2.5\, m / s$
• C. $V_{1}=5\, m / s , V _{2}=5\, m / s$
• D. None of these

Answer 1

Answer: (B)

According to the given equation
$First case:$ Separation between the trucks decreases at the rate of $10 m / s$. Due to the opposite relative motion of trucks towards each other-
$V _{1}+ V _{2}=10$ (condition given) $\ldots \ldots(1)$
$Second case:$ Separation between the trucks increases due to the opposite relative motion of trucks away from each other
$V _{1}- V _{2}=5 \ldots \ldots (2) $ (condition given)
From equation (1) and (2), we get
$V _{1}+ V _{2}=10$
$\frac{ V _{1}- V _{2}=5}{2 V _{1}=15}$
$V _{1}=7.5 \,m / s$