The wings on a stoncfly do not flap, and thus the insect...

The wings on a stoncfly do not flap, and thus the insect cannot fly. However, when the insect is on a water surface, it can sail across the surface by lifting its wings into a hreere. Suppose that you time stoneflies as they move at constant speed along a straight path of a certain length. On average, the trips each take $7.1 \mathrm{~s}$ with the wings set as sails and $25.0 \mathrm{~s}$ with the wings tucked in. (a) What is the ratio of the sailing speed $v_{s}$ to the nonsailing speed $v_{\sin } ?$ (b) In terms of $v_{s .}$ what is the difference in the times the inscets take to travel the first $2.0 \mathrm{~m}$ along the path with and without sailing?

Key Concepts

Constant Speed Motion

This concept refers to situations where an object travels at a fixed speed, meaning its velocity remains constant throughout the motion. The relationship between distance, speed, and time in such cases is given by the equation distance = speed × time, which is the fundamental equation used to analyze uniform motion.

Inverse Proportionality of Speed and Time

When an object travels a fixed distance at two different constant speeds, the speeds are inversely proportional to the times taken to cover that distance. This means that if the time taken for one speed is known, the speed can be related by the inverse ratio of the times, an important principle when comparing motions under different conditions.

Speed Ratios

Speed ratios involve comparing two different speeds by forming a ratio, particularly useful when the object covers the same distance at each speed. Because the time to cover the distance is inversely related to the speed, the ratio of the speeds can be determined by the reciprocal of the ratio of the times, providing a direct method to compare the efficiencies of different modes of motion.

Calculating Time Differences

This concept involves determining the difference in time taken to cover the same distance under different conditions. By applying the formula time = distance/speed for each scenario and then finding the difference, one can assess the impact of changes in speed, such as those arising from different means of propulsion or environmental factors.

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