Final answer:
The father and daughter both take 34.09 seconds to reach the bus stop. The daughter's total distance traveled is 119.315 meters, and if she ran in a straight line at the same average speed, she would have traveled 44.315 meters beyond the bus stop.
Step-by-step explanation:
The question involves calculating times and distances based on average speeds, which makes this a mathematics problem. To answer these kinds of questions, we use the formula distance = speed × time. Let's go step by step through each sub-question.
Part (a)
To find out how long it takes both the father and the daughter to reach the bus stop, we need to divide the distance each traveled by their respective average speeds. Since both arrived at the same time, we can set their times equal:
Time for father = Distance / Father's speed = 75 m / 2.2 m/s = 34.09 seconds
So, the father and the daughter both take 34.09 seconds to reach the bus stop.
Part (b)
For the daughter's total distance traveled, we use the formula distance = speed × time. We already know her time (same as the father's) and her speed:
Daughter's distance = Daughter's speed × time = 3.5 m/s × 34.09 s = 119.315 m
The daughter's total distance traveled is 119.315 meters.
Part (c)
If the daughter maintained her speed and traveled in a straight line, she would outpace the father. We use her speed to find out how far she would go in the same amount of time:
Daughter's straight-line distance = 3.5 m/s × 34.09 s = 119.315 m
Since the bus stop is 75 meters away, we subtract that to find the distance beyond the bus stop:
Distance beyond bus stop = 119.315 m - 75 m = 44.315 meters
The daughter would have traveled 44.315 meters beyond the bus stop.