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eset.\ now, predict what will happen if you change the velocity of the red truck so that it has a magnitude smaller than that of the green truck but is negative.
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the trucks will stick together after the collision and move to the left.
the trucks will stick together after the collision and not move.
the trucks will stick together after the collision and move to the right.
submit
part d
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eset.\ now, predict what will happen if you change the velocity of the red truck so that it has a magnitude smaller than that of the green truck but is positive.
view available hint(s)
the trucks will stick together after the collision and move to the right.
the trucks will stick together after the collision and not move.
the trucks will stick together after the collision and move to the left.
submit

Question

Accepted Answer

### For the first question (red truck velocity: smaller magnitude, negative):
# Brief Explanations:
When two objects stick together after a collision (perfectly inelastic collision), we use the principle of conservation of momentum. Let's assume the green truck has a positive velocity (say $ v_g $) and the red truck has a velocity $ v_r $ where $ |v_r| < v_g $ and $ v_r < 0 $ (negative, so direction opposite to green, likely left if green is right). The total initial momentum is $ m_gv_g + m_rv_r $. Since $ v_r $ is negative and its magnitude is less than $ v_g $, the total momentum will be positive (because $ m_gv_g $ (positive) has a larger magnitude than $ |m_rv_r| $ (negative contribution)). Wait, no—wait, maybe the green truck is moving right (positive) and red is moving left (negative). But if the magnitude of red's velocity is smaller than green's, the net momentum is $ m_gv_g - m_r|v_r| $. If we assume equal masses (common in such problems), then net momentum is $ v_g - |v_r| $, which is positive (since $ |v_r| < v_g $). Wait, no—wait, maybe I got the direction wrong. Wait, the options say "move to the right" or "left". Wait, maybe the green truck is moving right (positive), red is moving left (negative) but with smaller magnitude. So total momentum: $ m_gv_g + m_r(-|v_r|) $. If $ m_g = m_r $ (common in these simulations), then momentum is $ v_g - |v_r| $, which is positive (since $ |v_r| < v_g $), so the combined mass moves to the right? Wait, no—wait, maybe the initial setup: maybe green is moving right, red is moving left, but red's speed (magnitude) is smaller. Wait, no, the first question: red truck velocity is negative (so direction opposite to positive, say left) but magnitude smaller than green (which is positive, right). So total momentum: $ p_{total} = m_gv_g + m_rv_r $. If $ v_r $ is negative (left), $ v_g $ positive (right), and $ |v_r| < v_g $, and if masses are equal, $ p_{total} = v_g - |v_r| $, which is positive (since $ |v_r| < v_g $), so the combined mass moves to the right? Wait, no, the first option is "move to the left", second "not move", third "move to the right". Wait, maybe I messed up the direction. Wait, maybe the green truck is moving left (negative) and red is moving right (positive)? No, the problem says "red truck so that it has a magnitude smaller than that of the green truck but is negative". So green's velocity is positive (say right), red's is negative (left) with smaller magnitude. So total momentum: $ m_gv_g + m_r(-|v_r|) $. If $ m_g = m_r $, then $ p = v_g - |v_r| $, positive, so move right. But wait, the first question's options: the third option is "move to the right". Wait, no, the first question's options:

1. The trucks will stick together after the collision and move to the left.

2. The trucks will stick together after the collision and not move.

3. The trucks will stick together after the collision and move to the right.

Wait, maybe the green truck is moving left (negative) and red is moving right (positive)? No, the red's velocity is negative. So green is positive (right), red is negative (left) with smaller speed. So net momentum: rightward (since green's momentum is larger). So the combined mass moves right. So the correct option is the third one? Wait, no, maybe I have the direction reversed. Wait, maybe in the simulation, positive is left? No, usually positive is right. Wait, maybe the red truck is moving right (positive) but no, the problem says red's velocity is negative. Wait, maybe the initial setup: green truck is moving right (positive velocity), red truck is moving left (negative velocity) but with speed (magnitude) less than green's speed. So total momentum: $ m_gv_g + m_r(-v_r) $ where $ v_r < v_g $. If $ m_g = m_r $, then $ p = v_g - v_r $, which is positive (since $ v_r < v_g $), so the combined mass moves to the right. So the correct option is "The trucks will stick together after the collision and move to the right."

### For Part D (red truck velocity: smaller magnitude, positive):
# Brief Explanations:
Now, red truck's velocity is positive (same direction as green, say right) but with smaller magnitude than green's velocity. So total momentum is $ m_gv_g + m_rv_r $, both positive, and $ v_r < v_g $. If masses are equal, $ p = v_g + v_r $, which is positive (rightward). So the combined mass moves to the right. The options are:

1. The trucks will stick together after the collision and move to the right.

2. The trucks will stick together after the collision and not move.

3. The trucks will stick together after the collision and move to the left.

So the correct option is the first one.

# Answer (for the first question):
3. The trucks will stick together after the collision and move to the right.

# Answer (for Part D):
1. The trucks will stick together after the collision and move to the right.

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QUESTION IMAGE

Question

Explanation:

For the first question (red truck velocity: smaller magnitude, negative):

Answer: