Question
When walking on ice, one should take short steps rather than long steps. Why?
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Answer
Let R represent the reaction offered by the ground. The vertical component $\text{R}\cos\theta$will balance the weight of the person and the horizontal component $\text{R}\sin\theta$ will help the person to walk forward.
Now, normal reaction $=\text{R}\cos\theta$
Friction force $=\text{R}\sin\theta$
Coefficient of friction,
$\mu=\frac{\text{R}\sin\theta}{\text{R}\cos\theta}=\tan\theta$
In a long step, $\theta$ is more. So tan $\theta$ is more. But µ has a fixed value. So, there is danger of slipping in a long step.
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