An iceberg breaks off from the Antarctic continent and floats due north at constant velocity/ It's latitude south decreases by 1 degree in 8 days. Taking the circumference of the earth to be 40 000km, calculate the speed of iceberg in ms^-1.
Hint:
Circumference=40000km
radius, r
= 40000/(2π) km
= 40000/(2π)*1000 m
angular speed, ω
= 1 degree/8 days
= (π/180)rad. / (8*86400) sec.
terrestrial speed
= rω
I get less than a metre per second.
To calculate the speed of the iceberg, we need to determine the distance it travels in meters and the time it takes in seconds. We can use the information given to find the distance.
The iceberg's latitude decreases by 1 degree in 8 days. Since we know the circumference of the Earth is 40,000 km, we can divide this value by 360 to find the distance covered by a change of 1 degree in latitude.
Distance covered by 1 degree = 40,000 km / 360 = 111.11 km
Now we will convert this distance from kilometers to meters by multiplying by 1000.
Distance covered by 1 degree = 111.11 km * 1000 = 111,110 meters
Therefore, the iceberg covers a distance of 111,110 meters for every 1-degree decrease in latitude.
Since we are given that the iceberg's latitude decreases by 1 degree in 8 days, we can calculate the speed by dividing the distance by the time.
Speed = Distance / Time
Speed = 111,110 meters / 8 days
However, we need to convert the time from days to seconds, as we want the speed in m/s. Since there are 24 hours in a day and 60 minutes in an hour, there are 24 * 60 * 60 = 86,400 seconds in a day.
Time = 8 days * 86,400 seconds/day = 691,200 seconds
Now, we can calculate the speed:
Speed = 111,110 meters / 691,200 seconds
Speed ≈ 0.1607 m/s
Therefore, the speed of the iceberg is approximately 0.1607 m/s.