Question

The ocean is eroding land from a coastal town at a rate of 0.01 mi^2/year. How many m^2/s is this? (365 days = 1 year, and 1.0 mile = 1,609 m)

A track athlete runs 1600 m race which is 4 laps around a 400 m track. She runs the first 3 laps (1,200 m) at an average speed of 3.8 m/s, and the last lap at an average speed of 5.3 m/s. What is her average speed for the entire race?

Answer 1

1)

eroding rate = 0.01 mi^2/year

using , 1 mi = 1609 m

1 year = 365 days

1 year = 365*24*60*60 seconds

= 0.01 * (1609m)^2/(365*24*60*60 sec)

= 0.000821 m^2/s

2)

time taken for first three laps = distance / speed

= 1200/3.8

= 315.79 sec

time taken for last lap = distance/speed

= 400/5.3

= 75.47 seconds

therefore, total time taken = 315.79 + 75.47

= 391.26 seconds

total distance = 1600 m

overall average speed = distance/time

= 1600/391.26

= 4.09 m/s

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