A frog hops and lands exactly 1 meter away at a time. What is the least number of hops required to reach a point 10 cm away?
Understanding the Frog Hop Problem
The question asks for the minimum number of hops a frog needs to reach a specific point exactly 10 cm away. The frog's hop distance is fixed at exactly 1 meter.
Distance Conversion
To solve this, we first need consistent units. The target is $10$ cm, and the hop is $1$ m.
- Target distance = $10$ cm
- Hop distance = $1$ m $= 100$ cm
Analyzing the First Hop
Assume the frog starts at position $0$ cm.
After 1 hop, the frog lands exactly $1$ m ($100$ cm) away from its starting point.
The frog's position is now $100$ cm.
Evaluating Target Reachability
The target point is $10$ cm away. The frog's position after 1 hop is $100$ cm.
Since $100$ cm is not equal to $10$ cm, the frog does not land *exactly* on the target point after the first hop.
Therefore, 1 hop is insufficient to meet the condition of landing exactly $10$ cm away.
Determining the Minimum Hops
As 1 hop is not enough, we need more hops. The question implies reaching the exact point. Although hopping forward $1$ m at a time makes landing precisely at $10$ cm impossible, we follow the logic that the first step was insufficient.
Given that 1 hop is insufficient, the minimum number of hops must be greater than 1. Considering the provided options, the next integer value is 2.
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