Reflecting on Momentum: Karen and David's Speed Comparison
How do Karen and David's speeds compare after they push off?
A. Karen's speed is the same as David's speed.
B. Karen's speed is one-fourth of David's speed.
C. Karen's speed is one-third of David's speed.
D. Karen's speed is four times David's speed.
E. Karen's speed is three times David's speed.
Answer
Both Karen and David have a speed of zero after the push-off due to the conservation of momentum.
According to the law of conservation of momentum, the total momentum before and after the push-off should be equal. Initially, both Karen and David are at rest, so the total momentum before the push-off is zero. After the push-off, the total momentum should still be zero.
Let's denote Karen's mass as m and David's mass as 3m (given that David's mass is three times that of Karen).
If Karen moves with a speed v, the total momentum after the push-off is given by:
(3m) × (0) + m × (-v) = 0
Simplifying the equation:
-mv = 0
Since the mass (m) cannot be zero, the only possible solution is v = 0.
Therefore, Karen's speed is zero after the push-off. On the other hand, David's mass is three times that of Karen, so his speed after the push-off would also be zero.
In conclusion, both Karen and David's speeds are zero after the push-off.