Ice skaters Jerry (73.6 kg) and Rachel (38 kg) initially stand at rest, Rachel pusties Jerry with a force of 59.3 N for 0.224 5. What is Rachel’s speed (relative to ground as they move away from each other? The friction is negligible.
The Correct Answer and Explanation is :
Rachel’s speed relative to the ground after pushing Jerry is 0.35 m/s.
Explanation:
The problem involves two ice skaters, Jerry and Rachel, initially at rest. Rachel pushes Jerry, and we need to determine Rachel’s speed after the push.
Concepts Used:
- Newton’s Third Law of Motion: When Rachel exerts a force on Jerry, Jerry exerts an equal and opposite force on Rachel.
- Impulse-Momentum Theorem: The impulse applied to an object equals the change in momentum of that object. [
\text{Impulse} = \text{Force} \times \text{Time}
] [
\Delta p = m v – m u
] Since the initial velocity ( u ) is 0 (both start from rest), [
F t = m v
] Rearranging for velocity: [
v = \frac{F t}{m}
]
Calculation for Rachel’s Velocity:
- Given force ( F = 59.3 ) N
- Time duration ( t = 0.224 ) s
- Rachel’s mass ( m = 38.0 ) kg
[
v = \frac{(59.3)(0.224)}{38.0}
]
[
v \approx 0.35 \text{ m/s}
]
Thus, Rachel moves away from Jerry at 0.35 m/s in the opposite direction.
Now, I will generate an image representing the motion of Jerry and Rachel after the push.
Here is the image of Jerry and Rachel pushing away from each other on the ice rink. It visually represents their movement after the push, with Jerry moving slowly and Rachel moving faster in the opposite direction. Let me know if you need any modifications!