5. A 3 kg ball is dropped onto a concrete floor. What is the magnitude of the ball's change in momentum if its speed just before striking the floor is $$ 7 \mathrm{~m} / \mathrm{s} $$ and its rebound speed is $$ 3 \mathrm{~m} / \mathrm{s} $$ ? A. $$ 10 \mathrm{~kg}-\mathrm{m} / \mathrm{s} $$ B. $$ 15 \mathrm{kg-m} / \mathrm{s} $$ C. $$ 30 \mathrm{~kg}-\mathrm{m} / \mathrm{s} $$ D. $$ 60 \mathrm{~kg}-\mathrm{m} / \mathrm{s} $$ 6. A 3.0 kg toy truck moves freely along a track at $$ 2.0 \mathrm{~m} / \mathrm{s} $$ and collides with a 1.0 kg toy car that is at rest. After the collision, the two cars stick together. What is their velocity after the collision? A. $$ 1.5 \mathrm{~m} / \mathrm{s} $$ B. $$ 2.0 \mathrm{~m} / \mathrm{s} $$ C. $$ 2.5 \mathrm{~m} / \mathrm{s} $$ D. $$ 3.0 \mathrm{~m} / \mathrm{s} $$

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UpStudy AI · Accepted Answer

We have a ball with mass $$ m = 3 \, \text{kg} $$. The speed just before striking the floor is $$ v_i = 7 \, \text{m/s} $$ (downward), and the rebound speed is $$ v_f = 3 \, \text{m/s} $$ (upward).
The initial momentum $$ p_i $$ is given by $$ p_i = m \cdot v_i $$ and the final momentum $$ p_f $$ is given by $$ p_f = m \cdot (-v_f) $$ (negative because it's in the opposite direction).
The change in momentum $$ \Delta p $$ is calculated as $$ \Delta p = p_f - p_i $$.
tions 
1. Calculate $$ p_i = 3 \cdot 7 $$.
2. Calculate $$ p_f = 3 \cdot (-3) $$.
3. Calculate $$ \Delta p = p_f - p_i $$.

Let's perform these calculations.

1. $$ p_i = 3 \cdot 7 $$
2. $$ p_f = 3 \cdot (-3) $$
3. $$ \Delta p = p_f - p_i $$
Calculate the value by following steps:
- step0: Calculate:
  $$3\times 7$$
- step1: Multiply the numbers:
  $$21$$
Calculate or simplify the expression $$ 3*(-3) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$3\left(-3\right)$$
- step1: Use the rules for multiplication and division:
  $$-3\times 3$$
- step2: Multiply the numbers:
  $$-9$$
Calculate or simplify the expression $$ -9-21 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$-9-21$$
- step1: Subtract the numbers:
  $$-30$$
We have a toy truck with mass $$ m_1 = 3.0 \, \text{kg} $$ moving at speed $$ v_1 = 2.0 \, \text{m/s} $$ and a toy car with mass $$ m_2 = 1.0 \, \text{kg} $$ at rest ($$ v_2 = 0 \, \text{m/s} $$).
The total momentum before the collision is equal to the total momentum after the collision. The equation is given by:

$$
m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_f
$$

where $$ v_f $$ is the final velocity after the collision.
Rearranging the equation gives:

$$
v_f = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2}
$$

Now, substituting the values into the equation:1. $$ v_f = \frac{3.0 \cdot 2.0 + 1.0 \cdot 0}{3.0 + 1.0} $$

Let's perform this calculation.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(3\times 2+1\times 0\right)}{\left(3+1\right)}$$
- step1: Multiply:
  $$\frac{\left(3\times 2+0\right)}{\left(3+1\right)}$$
- step2: Remove the parentheses:
  $$\frac{3\times 2+0}{3+1}$$
- step3: Multiply the numbers:
  $$\frac{6+0}{3+1}$$
- step4: Remove 0:
  $$\frac{6}{3+1}$$
- step5: Add the numbers:
  $$\frac{6}{4}$$
- step6: Reduce the fraction:
  $$\frac{3}{2}$$
The velocity of the two cars after the collision is $$ 1.5 \, \text{m/s} $$, which corresponds to option A.

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