A large truck of mass 3600 kg approaches a car of mass 1250 kg traveling in the opposite direction.If the velocity of the center of mass of the system is zero,and the truck's speed is 18 m/s,how fast is the car moving?
A)52 m/s
B)6.3 m/s
C)70 m/s
D)31 m/s

Question

Quizplus · Accepted Answer

The velocity of the center of mass (Vcm) of a system is given by the formula: $V_{cm} = \frac{m_1v_1 + m_2v_2}{m_1 + m_2}$, where $m_1$ and $m_2$ are the masses of the two objects, and $v_1$ and $v_2$ are their velocities, respectively. Given that $V_{cm} = 0$, $m_1 = 3600$ kg, $v_1 = 18$ m/s (since they are moving in opposite directions, one velocity is positive and the other is negative), and $m_2 = 1250$ kg, we can solve for $v_2$.Setting up the equation with the given values and solving for $v_2$, we get:$$0 = \frac{3600 \times 18 + 1250 \times v_2}{3600 + 1250}$$Solving for $v_2$, we find that $v_2 = -52$ m/s. The negative sign indicates that the car is moving in the opposite direction to the truck, which matches the problem statement. Therefore, the car's speed is 52 m/s.

A Large Truck of Mass 3600 Kg Approaches a Car