calculate height of minute hand?

Question

hi all

The height (h) in metres above ground of a tip of minute hand can be modelled with this equation

h = 90 + 3.5 sin ( pi * t / 30 + pi / 2 )

calculate height above ground when the tip of minute hand is at 20 minutes past midnight.

i get the answer 88.25 m but i think it is wrong.

my working is:

90 + 3.5 sin ( pi * 20 / 30 + pi / 2) i took the height as 20, as the minute hand was at 20 past midnite. hence only 20 mins if we take the 24 hr clock 00.20 so used 20 as the height.

any help appreciated.

Thanks
l1khs

Answer 1

t is not the height. It is the time in minutes.

But for that what you have replaced t by 20 minutes is correct.


sin ( pi * 20 / 30 + pi / 2) = -0.50

Hence the answer is 90 - 3.5*0.50 = 88.25

Your answer is correct.

If we put t = 0 in the above equation we get

sin ( pi * 0 + pi / 2) = 1.

Thus the maximum height is 90 + 3.5 when the minuute hand is at 12.

If we put t = 15 in the above equation we get
sin ( pi * 15/30 + pi / 2) = 0, and the height is 90.
The minute hand is against the number 3 in the clock.

If we put t = - 15 in the above equation we get
sin ( pi *[ -15/30] + pi / 2) = 0, and the height is 90.
The minute hand is against the number 9 in the clock.

If we put t =30 in the above equation we get
sin ( pi *[ -30/30] + pi / 2) = -1 , and the height is 90 - 3.5
The minute hand is against the number 9 in the clock


Hence your answer is correct.

Answer 2

I think that you are right about h = 90 + 3.5 sin ( pi * 20 / 30 + pi / 2), though I do not understand what you mean in "i took the height as 20".
The reason is from understanding of the sine function, it is maximum at sin(pi/2), sin (5pi/2), sin (9pi/2), .... and minimum at sin(3pi/2), sin (7pi/2),...So it is obvious that h is maximized when t = 0, 60, 120, ..., and minimized when t = 30, 90, 150, ....

Answer 3

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