two carts with different masses are both moving to the right. the mass and initial velocity of each cart are…

two carts with different masses are both moving to the right. the mass and initial velocity of each cart are shown in the diagram. v1 = 2.0 m/s, v2 = 1.0 m/s, m1 = 1.2 kg, m2 = 0.5 kg. the carts then collide and stick together. drag and drop the correct speed and direction of the carts after the collision. put the direction in the top box and the speed in the lower box. drag & drop the answer 3.0 m/s, →, ←, 1.7 m/s, 1.5 m/s

two carts with different masses are both moving to the right. the mass and initial velocity of each cart are shown in the diagram. v1 = 2.0 m/s, v2 = 1.0 m/s, m1 = 1.2 kg, m2 = 0.5 kg. the carts then collide and stick together. drag and drop the correct speed and direction of the carts after the collision. put the direction in the top box and the speed in the lower box. drag & drop the answer 3.0 m/s, →, ←, 1.7 m/s, 1.5 m/s

Answer

Explanation:

Step1: Apply conservation of momentum

The formula for conservation of momentum is $m_1v_1 + m_2v_2=(m_1 + m_2)v_{f}$. Here, $m_1 = 1.2$ kg, $v_1=2.0$ m/s, $m_2 = 0.5$ kg and $v_2 = 1.0$ m/s.

Step2: Calculate the left - hand side

$m_1v_1+m_2v_2=(1.2\times2.0)+(0.5\times1.0)=2.4 + 0.5=2.9$ kg·m/s.

Step3: Calculate the total mass

$m_1 + m_2=1.2+0.5 = 1.7$ kg.

Step4: Solve for the final velocity

$v_{f}=\frac{m_1v_1 + m_2v_2}{m_1 + m_2}=\frac{2.9}{1.7}\approx1.7$ m/s. Since the initial velocities are to the right and the final velocity is positive, the direction is to the right.

Answer:

Direction: $\rightarrow$ Speed: $1.7$ m/s