Question

a 1000kg truck has an initial velocity of 50m/s. a 500kg car has an initial velocity of 60m/s and travels in the same direction. if the car runs into the back of the truck and sticks to it, what is the new velocity they are traveling at?

Explanation:

Step1: Apply conservation of momentum

The formula for conservation of momentum is $m_1v_1 + m_2v_2=(m_1 + m_2)v$. Here, $m_1 = 100\ kg$ (mass of truck), $v_1=50\ m/s$ (initial - velocity of truck), $m_2 = 50\ kg$ (mass of car), and $v_2 = 80\ m/s$ (initial - velocity of car).

Step2: Substitute values into the formula

$(100\times50)+(50\times80)=(100 + 50)v$. First, calculate the left - hand side: $100\times50=5000$ and $50\times80 = 4000$. So, $5000+4000=9000$. The right - hand side is $150v$.

Step3: Solve for $v$

We have the equation $9000 = 150v$. Divide both sides by 150: $v=\frac{9000}{150}=60\ m/s$.

Answer:

$60\ m/s$