Watch Hands
January 28th, 2009
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Fossil Three Hand MOP Dial Watch List Price: $85.00 Sale Price: $56.23 Average Rating:   |
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Free Standard Shipping Over $100. Always arrive on time with this sleek, stainless steel watch. Silver-tone links create a classic bracelet that holds a stainless steel case. The white pearlized dial gives this watch a modern look you'll love, while the date window adds extra functionality... |
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Calculus Related Rates, Watch Hands?
The minute hand on a watch is 6 mm long and the hour hand is 3 mm long. How fast is the distance between the tips of the hands changing at one o'clock?
D^2 = 6^2 + 3^2 - 2*6*3cos x
= 36 + 9 - 36cos x
= 45 - 36cos x
differentiated,
2D dD = 36sin x dx
dD/dx = 36sin x / 2D = 18sin x / D
at 1 o'clock, x = π/6
dx/dt = 30*/hour (of hour hand) - 360*/hour (of minute hand)
= 0.5*/minute - 6*/minute
= -5.5*/minute
dD/dt = dD/dx * dx/dt
= [18sin 30* / D] * [-5.5]
= [18(0.5) / √(45 - 18√3)] * -5.5
= -13.31382 mm/minute
negative dD/dt means the distance is closing (becoming closer).
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