Question

An airplane leaves Chicago and makes the 3000-km trip to Los Angeles in 5.0 h. A second plane leaves Chicago one-half hour later and arrives in Los Angeles at the same time. Compare the average velocities of the two planes. Ignore the curvature of Earth and the difference in altitude between the two cities.

a) The same
b) Second plane is faster
c) First plane is faster
d) Cannot be determined

Answer 1

The second plane, with an average velocity of 666.67 km/h, is faster than the first plane, which has an average velocity of 600 km/h, because it departed later but arrived simultaneously with the first plane.

Step-by-step explanation:

To compare the average velocities of the two planes, we first calculate the average velocity of the first plane. The first plane travels a distance of 3000 km in 5 hours, so its average velocity is:

• V_{1st} = distance/time = 3000 km / 5 h = 600 km/h.

The second plane leaves half an hour later and arrives at the same time. Since the total time for the second plane is 4.5 hours, we calculate its average velocity as follows:

• V_{2nd} = distance/time = 3000 km / 4.5 h = 666.67 km/h.

Thus, the second plane is faster than the first plane since it had a higher average velocity to catch up and arrive at the same time.