Solution
x(t) = 8 cos t, x(5π/6)= 8 cos(<span>5π/6)
</span>cos(5π/6)=cos(3π/6 + 2π/6 )=cos(π/3 +π/2)= - sin π/3 (cos (x+<span>π/2)= -sinx)
</span>x(t) = -8sin <span>π/3 = - 4 .sqrt3
</span>v(t) = -8sint = -8sin (π/3 +<span>π/2)= -8 cosπ/3 </span>(sin (x+π/2)= cosx)
v(t) =<span> -8 cosπ/3 = -8/2= - 4
</span>a(5π/6) = - 8cost = -(- sin π/3)= 4 .<span>sqrt3
</span>a(5π/6) = 4 .<span>sqrt3</span>
Answer:
v<em>min</em> = 0.23 m/s
Explanation:
The golf ball must travel a distance equal to its diameter in the time between blade arrivals to avoid being hit. If there are 12 blades and 12 blade openings and they have the same width, then each blade or opening is 1/24 of a circle of is 2π/24 = 0.26 radians across.
Therefore, the time between the edge of one blade moving out of the way and the next blade moving in the way is
time = angular distance/angular velocity
⇒ t = 0.26 rad / 1.35 rad/s = 0.194 s
The golf ball must get completely through the blade path in this time, so must move a distance equal to its diameter in 0.194 s, therefore the speed of the golf ball is
v =d/t
⇒ v = 0.045 m / 0.194 s = 0.23 m/s
To determine your line of latitude , you would need to know the angle your location (line) makes with the equatorial plane at earth's center.
<h3>What is Line of latitude?</h3>
This is also referred to as parallels and it is defined as the imaginary lines that divide the Earth. They run from east to west and are used to specify the north and south sides of the Earth.
To determine the line of latitude , it is imperative to know the angle your location (line) makes with the equatorial plane at earth's center which is therefore the reason why it was chosen as the most appropriate choice.
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