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Zorluk: ZorRelative Motion and Catch-Up Scenarios

A commercial cargo flight leaves an airport at 06:00 AM, heading due east at a constant cruising speed of 300300 mph. At 07:30 AM, a passenger jet leaves the same airport, flying along the exact same route at a constant cruising speed of 600600 mph. At what time will the passenger jet catch up to the cargo flight?

  1. A
    08:00 AM
  2. B
    08:30 AM
  3. 09:00 AMCevap
  4. D
    09:20 AM

Cevap

09:00 AM
The cargo flight has a 1.51.5-hour head start, covering 450450 miles (300 mph×1.5 hours300 \text{ mph} \times 1.5 \text{ hours}). Because both aircraft are traveling in the same direction, the passenger jet closes this gap at a relative speed of 300300 mph (600 mph−300 mph600 \text{ mph} - 300 \text{ mph}). It takes the passenger jet 1.51.5 hours to close the 450450-mile gap (450÷300=1.5450 \div 300 = 1.5). Adding 1.51.5 hours (11 hour and 3030 minutes) to the passenger jet's departure time of 07:30 AM gives a final catch-up time of 09:00 AM.

Adım Adım Çözüm

1
Calculate the time difference between the departures.
1.51.5 hours.
From 06:00 AM to 07:30 AM is exactly 11 hour and 3030 minutes, or 1.51.5 hours. This determines how long the cargo flight traveled before the passenger jet departed.
2
Calculate the head-start distance of the cargo flight.
450450 miles.
Using Distance = Rate ×\times Time, multiply the cargo flight's speed by its head-start time: 300 mph×1.5 hours=450 miles300 \text{ mph} \times 1.5 \text{ hours} = 450 \text{ miles}.
3
Determine the relative speed of the two aircraft.
300300 mph.
Because both aircraft are traveling in the same direction, subtract the slower speed from the faster speed to find how quickly the gap is closing: 600 mph−300 mph=300 mph600 \text{ mph} - 300 \text{ mph} = 300 \text{ mph}.
4
Calculate the time required for the passenger jet to catch up.
1.51.5 hours.
Divide the head-start distance by the relative speed: 450 miles÷300 mph=1.5 hours450 \text{ miles} \div 300 \text{ mph} = 1.5 \text{ hours}.
5
Add the catch-up time to the passenger jet's departure time.
09:00 AM.
1.51.5 hours is 11 hour and 3030 minutes. Adding this to 07:30 AM gives 09:00 AM.

Anahtar Kavram

Relative Motion (Same Direction)
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Relative Motion and Catch-Up Scenarios

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