Question

Please check my work for:

The minute hand of a steeple clock is 4 feet long, and the hour hand is 3 feet long. How fast is the distance between the tips of the hands changing at 3 o'clock. (Hint says to use the law of cosines to computer the distance between the tips of the hands. Also, I determined that the relative rates of change of the angle between the two hands is -11(pi)/6 at 3 o'clock.

Answer 1

I came up with 22(pi)/5 feet per hour, but logically, that number looks double what it should be

Answer 2

I agree with the -11 pi/6, but I get -11 pi/5 for the answer

Answer 3

I'll upload my work in a sec, if you wouldn't mind taking a look

Answer 4

I had previously posted this same question, and another individual also came up with the answer that you did...which makes me worry

Answer 5

@NoelGreco what do you think...see any problems with my work?

Answer 6

Actually, I found my mistake when checking your work, and I agree with your answer. Remember, these are pretty long arms and a rate of ~70 ft/hr doesn't seem ridiculous. I'll check it one more time after walking the dogs. I'll also try it using vectors and no angles since the minute hand is going due east at its tangential velocity, and the hour hand's going due south

Answer 7

right, that rate of change may be very fast, since it's going at such an angle