9. momentum which has more momentum, a truck that is parked or a falling raindrop? explain.
10. momentum is the momentum of a car traveling south different from that of the same car when it travels north at the same speed? draw the momentum vectors to support your answer.
11. impulse and momentum when you jump from a height to the ground, you bend at the knees as your feet hit the floor. explain why you do this in terms of impulse and momentum.
12. impulse and momentum a 0.174 - kg softball is pitched horizontally at 26.0 m/s. the ball moves in the opposite direction at 38.0 m/s after it is hit by the bat.
a. draw arrows showing the ball’s momentum before and after the bat hits it.
b. what is the change in momentum of the ball?
c. what is the impulse delivered by the bat?
d. if the bat and ball are in contact for 0.80 ms, what is the average force the bat exerts?
13. momentum the speed of a basketball is the same just before and after the ball hits the floor. are the impulse on and the change in momentum of the basketball zero when the ball hits the floor? if not, in which direction is the change in momentum? draw the ball’s momentum vectors before and after impact.
14. frame of reference why is momentum defined for a particular frame of reference? explain.

Question

9. momentum which has more momentum, a truck that is parked or a falling raindrop? explain.
10. momentum is the momentum of a car traveling south different from that of the same car when it travels north at the same speed? draw the momentum vectors to support your answer.
11. impulse and momentum when you jump from a height to the ground, you bend at the knees as your feet hit the floor. explain why you do this in terms of impulse and momentum.
12. impulse and momentum a 0.174 - kg softball is pitched horizontally at 26.0 m/s. the ball moves in the opposite direction at 38.0 m/s after it is hit by the bat.
    a. draw arrows showing the ball’s momentum before and after the bat hits it.
    b. what is the change in momentum of the ball?
    c. what is the impulse delivered by the bat?
    d. if the bat and ball are in contact for 0.80 ms, what is the average force the bat exerts?
13. momentum the speed of a basketball is the same just before and after the ball hits the floor. are the impulse on and the change in momentum of the basketball zero when the ball hits the floor? if not, in which direction is the change in momentum? draw the ball’s momentum vectors before and after impact.
14. frame of reference why is momentum defined for a particular frame of reference? explain.

Accepted Answer

### Question 9
# Brief Explanations:
Momentum is defined as $p=mv$. A parked truck has a velocity $v=0$, so its momentum is 0. A falling raindrop has a non-zero velocity and non-zero mass, so it has positive momentum.
# Answer:
The falling raindrop has more momentum. The parked truck has a velocity of 0, so its momentum $p=mv=0$, while the raindrop has a non-zero velocity and mass, giving it a positive momentum.

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### Question 10
# Brief Explanations:
Momentum is a vector quantity, meaning it has both magnitude and direction. The two cars have the same speed (same magnitude of momentum) but opposite directions, so their momentum vectors are equal in length but point north and south.
# Answer:
Yes, the momentum is different. Momentum is a vector: the car traveling north has momentum vector pointing north, and the car traveling south has a momentum vector pointing south, even though their magnitudes ($p=mv$) are equal.
- Momentum vector (north): Arrow pointing north, length proportional to $mv$
- Momentum vector (south): Arrow pointing south, length proportional to $mv$

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### Question 11
# Brief Explanations:
Impulse $J=\Delta p = F\Delta t$. Bending knees increases the time $\Delta t$ of impact. Since the change in momentum $\Delta p$ (from falling to rest) is fixed, increasing $\Delta t$ reduces the average force $F$ exerted on the body, preventing injury.
# Answer:
Bending knees increases the time of impact. By the impulse-momentum theorem $J=\Delta p=F\Delta t$, with fixed $\Delta p$ (stopping from fall), a larger $\Delta t$ reduces the force $F$ on your body, minimizing injury risk.

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### Question 12
# Explanation:
## Step1: Define coordinate system
Let the initial pitch direction be positive. $m=0.174\ 	ext{kg}$, $v_i=26.0\ 	ext{m/s}$, $v_f=-38.0\ 	ext{m/s}$ (negative for opposite direction)
## Step2: Calculate initial and final momentum
Initial momentum: $p_i = mv_i = 0.174 	imes 26.0$
Final momentum: $p_f = mv_f = 0.174 	imes (-38.0)$
## Step3: Find change in momentum
$\Delta p = p_f - p_i = m(v_f - v_i)$
$\Delta p = 0.174(-38.0 - 26.0) = 0.174(-64.0)$
## Step4: Impulse equals $\Delta p$
Impulse $J=\Delta p$
## Step5: Calculate average force
$J=F\Delta t$, so $F=\frac{J}{\Delta t}$. Convert $\Delta t=0.80\ 	ext{ms}=0.80	imes10^{-3}\ 	ext{s}$
# Answer:
a. (Diagram): Arrow pointing in initial pitch direction (right) for $p_i$, arrow pointing left (opposite direction) for $p_f$, with $p_f$ longer than $p_i$.
b. Change in momentum: $\Delta p = -11.1\ 	ext{kg·m/s}$ (negative sign indicates direction opposite to initial pitch)
c. Impulse delivered by the bat: $J = -11.1\ 	ext{kg·m/s}$ (same as change in momentum)
d. Average force: $F=\frac{-11.1}{0.80	imes10^{-3}} = -1.4	imes10^4\ 	ext{N}$ (negative sign indicates force direction opposite to initial pitch)

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### Question 13
# Brief Explanations:
Momentum is $p=mv$. The ball has the same speed before and after impact, but direction reverses (down before impact, up after). So momentum is not zero (direction changes, so $\Delta p
eq 0$). Impulse equals change in momentum, so impulse is non-zero, directed upward.
# Answer:
No, the basketball's momentum is not zero after impact: its speed is the same but direction is reversed (upward instead of downward). The change in momentum is $\Delta p = mv_f - mv_i = m(v - (-v))=2mv$, directed upward.
- (Diagram): Downward arrow (before impact) and upward arrow (after impact) of equal length for momentum vectors.

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### Question 14
# Brief Explanations:
Momentum depends on velocity, and velocity is only defined relative to a chosen frame of reference (e.g., stationary ground vs moving car). A object at rest in one frame has zero momentum, but has non-zero momentum in a moving frame.
# Answer:
Momentum is $p=mv$, and velocity $v$ is measured relative to a specific frame of reference. An object's velocity (and thus momentum) changes depending on the observer's frame, so momentum must be defined for a particular frame.

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