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. $$ 60 \mathrm{kg-m} / \mathrm{s} $$

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UpStudy AI · Accepted Answer

We have the following values:
- Mass of the ball, $$ m = 3 \, \text{kg} $$
- Speed just before striking the floor, $$ v_i = 7 \, \text{m/s} $$ (downward)
- Rebound speed, $$ v_f = 3 \, \text{m/s} $$ (upward)
The change in momentum ($$ \Delta p $$) can be calculated using the formula:
$$
\Delta p = p_f - p_i
$$
where:
- $$ p_i = m \cdot v_i $$ (momentum before impact)
- $$ p_f = m \cdot (-v_f) $$ (momentum after impact, negative because it's in the opposite direction)

Now, let's calculate $$ p_i $$ and $$ p_f $$.
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:
  $$-9$$
Now we have:
- $$ p_i = 21 \, \text{kg-m/s} $$
- $$ p_f = -9 \, \text{kg-m/s} $$

Now, we can calculate the change in momentum:
$$
\Delta p = p_f - p_i = -9 - 21
$$
Calculate the value by following steps:
- step0: Calculate:
  $$-9-21$$
- step1: Subtract the numbers:
  $$-30$$
The magnitude of the ball's change in momentum is $$ 30 \, \text{kg-m/s} $$. Therefore, the answer is C. $$ 30 \, \text{kg-m/s} $$.

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 and its rebound speed is ?
A.
B.
C.
D.

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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 and its rebound speed is ? A. B. C. D.