Respuesta :
Answer:
The linear speed is [tex]1,130.4\frac{ft}{min}[/tex]
Step-by-step explanation:
step 1
Find the circumference of the circle
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=18\ ft[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]C=2(3.14)(18)[/tex]
[tex]C=113.04\ ft[/tex]
step 2
Find the linear speed in feet per minute
we know that
The wheel is rotating at 10 revolutions per minute
Convert revolutions to feet
Remember that
One revolution is equal to the circumference of the circle
so
10 revolutions is equal to
[tex](10)113.04=1,130.4\ ft[/tex]
therefore
The linear speed is [tex]1,130.4\frac{ft}{min}[/tex]
You can use the fact that as one rotation of the wheel will cover linear length equal to its circumference as its circumference is in the touch with water(think of it as if wheel is of a bicycle and its walking on road).
The linear speed of the specified wheel, in feet per minute, of the water is 1130.97 feet per minute
How to find the linear speed of a wheel?
You can use the fact that as one rotation of the wheel will cover linear length equal to its circumference as its circumference is in the touch with water(think of it as if wheel is of a bicycle and its walking on road and the fact that when one point of the wheel is touching the ground, and then that point after 1 full rotation comes to touch the ground, the length covered will be equal to the circumference as its whole circumference touched the ground in the mean time between two touches of same point.)
Using the above fact to find the linear speed of the vehicle
The specified wheel has radius of 18 feet.
The circumference of the wheel is calculated as
[tex]\text{Circumference} = 2 \pi r = 2 \times \pi \times 18 \approx 113.097 \: \rm feet[/tex]
This is the distance covered in one rotation.
Since the wheel is rotating 10 times in 1 minute, thus,
In 1 minute, the wheel will cover 10 times 113.097 feet distance.
Or the linear speed of the wheel = 1130.97 feet per minute
Thus,
The linear speed of the specified wheel, in feet per minute, of the water is 1130.97 feet per minute
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