Question

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

• A. $V_1=8.5m/s,V_2=1.5m/s$
• B. $V_1=7.5m/s,V_2=2.5m/s$
• C. $V_1=5m/s,V_2=5m/s$
• D. None of these

Answer 1

Answer: (B)

According to the given equation
$Firstcase:$ Separation between the trucks decreases at the rate of $10m/s$. Due to the opposite relative motion of trucks towards each other-
$V_1+V_2=10$ (condition given) $\dots \dots (1)$
$Secondcase:$ Separation between the trucks increases due to the opposite relative motion of trucks away from each other
$V_1-V_2=5\dots \dots (2)$ (condition given)
From equation (1) and (2), we get
$V_1+V_2=10$
$\frac{V_1-V_2=5}{2V_1=15}$
$V_1=7.5m/s$