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Answer :
The cyclist's total displacement is 18.8 km to the east.
To solve this problem, we can use the formula:
distance = speed × time
Given that the cyclist rides 6.4 km east for 17.4 minutes, we can calculate the speed as follows:
speed = distance / time
= 6.4 km / 17.4 minutes
Let's calculate the speed:
speed = 6.4 km / 17.4 minutes
≈ 0.36782 km/min
Since the cyclist is moving east, the velocity is positive. Therefore, the speed is 0.36782 km/min.
Next, the cyclist turns and heads west for 4.2 km in 5.1 minutes. The speed in this case is:
speed = distance / time
= 4.2 km / 5.1 minutes
≈ 0.82353 km/min
Since the cyclist is moving west, the velocity is negative. Therefore, the speed is -0.82353 km/min.
Finally, the cyclist rides east for 16.6 km, which takes 37.9 minutes. The speed can be calculated as:
speed = distance / time
= 16.6 km / 37.9 minutes
≈ 0.43799 km/min
Since the cyclist is moving east, the velocity is positive. Therefore, the speed is 0.43799 km/min.
Now that we have the speeds for each segment, we can determine the total displacement. Since east is the positive direction, we consider the distance traveled east as positive and the distance traveled west as negative.
Total displacement = distance east - distance west
The distance east is 6.4 km + 16.6 km = 23 km
The distance west is 4.2 km
Total displacement = 23 km - 4.2 km
= 18.8 km
Therefore, the cyclist's total displacement is 18.8 km to the east.
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