For one acre, multiply (4 × 104 feet2) by (meter / 3.28 feet (1 m))2, which equals 3,718 meters. ²
(104 meters) / (3,718 meters) = 2.69 acres per hectare (1 hectare / 1 acre).
The area of land that a yoke of oxen could plow in a day was the definition of the acre, an ancient unit of measurement.
Later, it was established to be one furlong by one chain, or 660 feet (201.17 m) by 66 feet (20.12 m). Its current measurement is 4,046.86 square meters.
4046.856 square meters make up an acre. But 1 hectare is equal to 100 meters by 100 meters, or 10,000 square meters. A hectare is hence larger than an acre (1 ha is equal to 2.47 acres).
An acre is a product of any rectangular land plot with a total area of 4,046 square meters, or 43,560 square feet (4,046.86 m²). Six plots of 6 × 120 feet (36.58 meters) (36.58 m) each make up an acre.
Therefore, 2.69 acres per hectare.
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b.) how long will it take for the swimmer to cross the river, if the distance from the starting point to the dock is 300 m?
Please show all your work, thanks
a)The direction that she must aim herself through the water to arrive at the dock will be 73.7°.
b)The time it takes for the swimmer to cross the river will be 240 seconds.
Speed is defined as the rate of change of the distance or the height attained. it is a time-based quantity. it is denoted by u for the initial speed while v for the final speed. its si unit is m/sec.
Given data;
The maximum speed of the swimmer In still water,v=1.25m/s.
Speed of river = 0.35m/s [E]
α is the direction that she must aim herself through the water to arrive at the dock.
t is the time it takes for the swimmer to cross the river
The distance from the starting point to the dock is,s = 300 m
If the swimmer were to swim straight, the water's speed along the x-axis would have to match that of the swimmer.
α is the angle between vx and v
The value of the
The time that the swimmer will use for reaching the dock;
s = V×t
t = s/(v)
t=300 m / 1.25 m/sec
t = 240 seconds
Hence, the direction that she must aim herself through the water to arrive at the dock. and it takes for the swimmer to cross the river will be 73.7° and 240 seconds respectively.
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Explanation:
As you can see in the picture, we want the swimmer to go on a straight line, so the speed of the water must be equal to the speed of the swimmer along the x-axis. We also know the value of v, so we can calculate the of the cosine of the angle (alpha) between Vx and V. Thanks to the fundamental relation of gioniometry (cos^2(x) + sin^2(x) = 1) we can find the sine of alpha and calculate Vy. With Vy we can calculate the time that the swimmer will use for reaching the dock: s = Vy * t => t = s/(Vy).
I'll let you do all the calculations, you just have to plug in values.