A child falls sideways off a sled while sledding on frictionless ice. What happens to the velocity of the sled?

Question

BlackTom AI · Accepted Answer

Conservation of horizontal momentum gives the key insight: with no external horizontal forces (frictionless ice), the total horizontal momentum of the child+sled system is constant.

Relevant concepts:
- Momentum p = m v, and for a system with no external horizontal forces, total horizontal momentum is conserved.
- "Falls sideways" implies the child's motion relative to the sled is perpendicular to the sled's forward direction, so there is no added forward or backward impulse.

Step-by-step reasoning:
1. Let M be the sled mass, m the child mass, and v0 the common forward velocity before the child falls off. Initial total horizontal momentum: P_initial = (M + m) v0.
2. After the child falls off, denote the sled forward velocity v_s and the child's horizontal component of velocity v_cx. Conservation of horizontal momentum requires:
   M v_s + m v_cx = (M + m) v0.
3. If the child simply falls sideways (no push forward or backward), the child's horizontal velocity component immediately after leaving the sled equals the original forward velocity v0: v_cx = v0. This is because no horizontal impulse changed the child’s forward speed.
4. Substitute v_cx = v0 into the momentum equation:
   M v_s + m v0 = (M + m) v0.
   Rearranging gives M v_s = M v0, so v_s = v0.
5. Therefore the sled’s forward velocity remains v0 — unchanged.

Why the other choices are incorrect:
- "It increases" or "It decreases": would require a net external horizontal impulse or a deliberate push/pull in the forward/backward direction between child and sled. Those are not present when the child falls sideways on frictionless ice.
- "Cannot be determined": incorrect because conservation of horizontal momentum provides a definite result under the stated conditions.

Conclusion: The sled’s velocity remains the same, which matches the provided correct answer: "It remains the same."

A child falls sideways off a sled while sledding on frictionless ice. What happens to the velocity of the sled?单项选择题

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